{"id":9894,"date":"2024-01-02T08:08:51","date_gmt":"2024-01-02T07:08:51","guid":{"rendered":"https:\/\/maschinenkanzlei.de\/machine-vibrations-resonances-and-vibrations-in-court-proceedings\/"},"modified":"2025-06-20T12:09:57","modified_gmt":"2025-06-20T10:09:57","slug":"machine-vibrations-in-court-proceedings","status":"publish","type":"post","link":"https:\/\/maschinenkanzlei.de\/en\/machine-vibrations-in-court-proceedings\/","title":{"rendered":"Machine vibrations, resonances and vibrations in court proceedings"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"9894\" class=\"elementor elementor-9894 elementor-9586\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a0e53d5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a0e53d5\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4e32a49\" data-id=\"4e32a49\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-86a7f4d elementor-widget elementor-widget-heading\" data-id=\"86a7f4d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">What is this article about?<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b0153ab elementor-widget elementor-widget-text-editor\" data-id=\"b0153ab\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>In the world of machines and technology, vibrations are a ubiquitous phenomenon and also \u201cfascinating\u201d for vibration experts. In this article you will learn why machine vibrations are always problematic and a \u201cspecial issue\u201d in court proceedings.<\/p><p>Vibrations can have a variety of effects, from noise to damage to equipment and machinery. This article briefly addresses the basics of structural dynamics and explains real problems in legal disputes. Oscillations in court proceedings are often part of the court&#8217;s evidentiary decision. This topic almost always leads to \u201c <i>interesting formulations<\/i> \u201d in relation to vibrations.<\/p><p>In addition, special aspects are highlighted that in reality represent a major problem before the responsible court in legal proceedings involving vibrations of machines: the burden of proof on the part of the party obliged to provide evidence and findings of fact by court experts in such disputes involving vibrations.<\/p><p>Immerse yourself in the fascinating world of machine oscillations, resonances and vibrations in mechanical engineering. Learn why this issue can sometimes become a legal arena.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b91c2af elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b91c2af\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-f502310\" data-id=\"f502310\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ec14594 elementor-widget elementor-widget-heading\" data-id=\"ec14594\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Short introduction to machine vibrations<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-03c233c elementor-widget elementor-widget-text-editor\" data-id=\"03c233c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>An extremely short introduction is necessary in order to give even technical laypeople a very, very small impression of the underlying physics and mathematics and thus the complexity of the topic of &#8221; <i>vibrations<\/i> &#8220;.<\/p><p>Figure 1 shows the result of the simulation of a nonlinear mathematical model, which depicts the essential physical properties of a car windshield wiper.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7844fcc elementor-widget elementor-widget-image\" data-id=\"7844fcc\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"800\" height=\"450\" src=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-0_0_Schwingung_800x450.jpg\" class=\"attachment-large size-large wp-image-9608\" alt=\"8 vibration vibration\" srcset=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-0_0_Schwingung_800x450.jpg 800w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-0_0_Schwingung_800x450-300x169.jpg 300w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-0_0_Schwingung_800x450-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Figure 1: Vibrations of the wiping lip of a car windshield wiper.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2730677 elementor-widget elementor-widget-text-editor\" data-id=\"2730677\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Figure 1 shows, even for laypeople, an oscillation curve over time, where \u201crepetitions\u201d can clearly be seen. So this is a good example of a simple definition of a vibration.<\/p><p>A vibration is a process in which&#8230;<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-c854e4c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c854e4c\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-db51c5\" data-id=\"db51c5\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-503f5729\" data-id=\"503f5729\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b5e0bec elementor-widget elementor-widget-text-editor\" data-id=\"b5e0bec\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>the variable of interest (distance, speed) changes over time in such a way that certain features recur.  <\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-7217f052\" data-id=\"7217f052\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-d9cdbd9 elementor-widget elementor-widget-heading\" data-id=\"d9cdbd9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">What vibrations are there?<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4a4da8a elementor-widget elementor-widget-text-editor\" data-id=\"4a4da8a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>A distinction is made between various different forms of vibrations, such as:<\/p><ul><li>free vibrations,<\/li><li>forced oscillations,<\/li><li>parameter-excited oscillations,<\/li><li>self-excited vibrations etc. .<\/li><\/ul><p>This short <a href=\"https:\/\/maschinenkanzlei.de\/en\/machine-newsletter-expert\/\" data-wpil-monitor-id=\"60\">article<\/a> cannot, of course, go into detail about the differences between the various vibration modes. Rather, essential features of an oscillatory system should be explained in the simplest possible terms.<\/p><p>Systems capable of oscillation are<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-a9e13a3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a9e13a3\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-653ff66\" data-id=\"653ff66\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-20eeb1d\" data-id=\"20eeb1d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d161572 elementor-widget elementor-widget-text-editor\" data-id=\"d161572\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>physically always structured the same way<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-14fc1dc\" data-id=\"14fc1dc\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-5fb4411 elementor-widget elementor-widget-text-editor\" data-id=\"5fb4411\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>and can generally always be described mathematically<\/p><ul><li>Dimensions,<\/li><li>rigidity,<\/li><li>Damping and if necessary<\/li><li>the stimulation of the system,<\/li><\/ul><p>if it is not a free system.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c80fadd elementor-widget elementor-widget-image\" data-id=\"c80fadd\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"300\" height=\"50\" src=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-Einmassenschwinger-300x50.png\" class=\"attachment-medium size-medium wp-image-9654\" alt=\"single-mass swing machine office\" srcset=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-Einmassenschwinger-300x50.png 300w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-Einmassenschwinger-600x101.png 600w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-Einmassenschwinger.png 604w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Equation 1<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-69f08a9 elementor-widget elementor-widget-text-editor\" data-id=\"69f08a9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Equation 1 now describes a forced oscillation for a damped 1-mass oscillator. It&#8217;s an extremely simple example. The natural frequency of this system can be easily determined from<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b94c5b8 elementor-widget elementor-widget-image\" data-id=\"b94c5b8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/elementor\/thumbs\/8-0-0_Eigenfrequenz-rah8lx9jxe6oo632vysaiancmijw9mb47bgpj5lnz4.png\" title=\"8-0-0_Eigenfrequenz\" alt=\"Eigenfrequenz\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-96e840d elementor-widget elementor-widget-text-editor\" data-id=\"96e840d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>These include:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-9981f6c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9981f6c\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-47ac4f7\" data-id=\"47ac4f7\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-690b9c1 elementor-widget elementor-widget-text-editor\" data-id=\"690b9c1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"text-align: right;\"><em>m:<\/em><\/p><p style=\"text-align: right;\"><em>d:<\/em><\/p><p style=\"text-align: right;\"><em>c:<\/em><\/p><p style=\"text-align: right;\"><em>f(t):<\/em><\/p><p style=\"text-align: right;\"><em>x**,x*,x:<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-aee8174\" data-id=\"aee8174\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9320608 elementor-widget__width-initial elementor-widget elementor-widget-text-editor\" data-id=\"9320608\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>(vibrating) mass;<\/p><p>Damping;<\/p><p>rigidity;<\/p><p>excitation of the vibration system;<\/p><p>Acceleration, speed, distance.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-bea68b2 elementor-widget elementor-widget-heading\" data-id=\"bea68b2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Resonance<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-04201a9 elementor-widget elementor-widget-text-editor\" data-id=\"04201a9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Figure 2 shows different magnification functions (resonance curves) purely as examples.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-20156dc elementor-widget elementor-widget-image\" data-id=\"20156dc\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"450\" src=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-0_Resonanz_800x450.jpg\" class=\"attachment-large size-large wp-image-9630\" alt=\"resonance damping machine law firm\" srcset=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-0_Resonanz_800x450.jpg 800w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-0_Resonanz_800x450-300x169.jpg 300w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-0_Resonanz_800x450-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Figure 2: Resonance curves.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-574a758 elementor-widget elementor-widget-text-editor\" data-id=\"574a758\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>In an oscillation system, the oscillation response increases the closer the excitation frequency approaches the natural frequency of the oscillation system. This connection is shown \u2013 purely as an example \u2013 in Figure 2.<\/p><p>In the \u201cundamped\u201d case, when the oscillation system is excited at the natural frequency, the oscillation response becomes \u201cinfinitely\u201d large. In \u201cdamped\u201d systems, the vibration response also increases significantly. Purely mathematically, it reaches \u201cfinite\u201d values. The greater the damping of the system, the smaller the increase in the resonance peak (also called resonance peak).<\/p><p>In general, this is understood as:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-07a6c30 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"07a6c30\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-77afe45\" data-id=\"77afe45\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-ee8ec73\" data-id=\"ee8ec73\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2b568d6 elementor-widget elementor-widget-text-editor\" data-id=\"2b568d6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>Resonance is the correspondence between natural frequency and interference frequency.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-c122ac0\" data-id=\"c122ac0\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-7e38ed6 elementor-widget elementor-widget-text-editor\" data-id=\"7e38ed6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>At this point it must be mentioned that in the damped system the resonance frequency does not coincide with the resonance frequency of the undamped oscillator.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-59b48bc elementor-widget elementor-widget-heading\" data-id=\"59b48bc\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Real vibration systems<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3ed243f elementor-widget elementor-widget-text-editor\" data-id=\"3ed243f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The main difference between theoretical models with few degrees of freedom and reality is that real oscillation systems have a<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-0a57ae5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0a57ae5\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-7716a2c\" data-id=\"7716a2c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-27eed6b\" data-id=\"27eed6b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8fbcd3b elementor-widget elementor-widget-text-editor\" data-id=\"8fbcd3b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>infinite number of degrees of freedom<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-a1f5a01\" data-id=\"a1f5a01\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-21a1fd7 elementor-widget elementor-widget-text-editor\" data-id=\"21a1fd7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>feature. This also results in<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-46f163e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"46f163e\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-4f62450\" data-id=\"4f62450\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-78bf8ee\" data-id=\"78bf8ee\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-decb0dd elementor-widget elementor-widget-text-editor\" data-id=\"decb0dd\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>infinitely many natural frequencies and natural shapes that always overlap in the vibration.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-59630ff\" data-id=\"59630ff\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-b878e5f elementor-widget elementor-widget-image\" data-id=\"b878e5f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/maschinenkanzlei.de\/en\/evidence-preservation-report-machines\/\">\n\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"451\" src=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-1_Maschinenschwingungen-Installationsfehler_800x450.jpg\" class=\"attachment-large size-large wp-image-9666\" alt=\"Machine vibrations Machine law firm\" srcset=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-1_Maschinenschwingungen-Installationsfehler_800x450.jpg 800w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-1_Maschinenschwingungen-Installationsfehler_800x450-300x169.jpg 300w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-1_Maschinenschwingungen-Installationsfehler_800x450-768x433.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Figure 1: Real damage caused by vibrations or machine vibrations.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5314d5f elementor-widget elementor-widget-heading\" data-id=\"5314d5f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Analytical approximation of the vibration system<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a68123e elementor-widget elementor-widget-text-editor\" data-id=\"a68123e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>When analyzing vibration systems, one tries to examine \u201conly\u201d the essential properties that need to be \u201cunderstood\u201d physically. This makes the effort bearable and can also be analyzed using today&#8217;s methods. First, a so-called <strong>physical replacement model<\/strong> is created. The <strong>mathematical model<\/strong> is ultimately derived from this, which can then be analyzed. This is ultimately done numerically. In general, with this approach there are \u201conly\u201d <em>n<\/em> degrees of freedom. Equation 2 shows how<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-8937873 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8937873\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-d59e11d\" data-id=\"d59e11d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-05a73eb\" data-id=\"05a73eb\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f5ee264 elementor-widget elementor-widget-text-editor\" data-id=\"f5ee264\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>Real systems result in exorbitantly large systems of equations.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-6c393b3\" data-id=\"6c393b3\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-ee00d70 elementor-widget elementor-widget-image\" data-id=\"ee00d70\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"429\" src=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-0-1_Schwingungssystem_800x429.jpg\" class=\"attachment-large size-large wp-image-9648\" alt=\"8 vibration system\" srcset=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-0-1_Schwingungssystem_800x429.jpg 800w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-0-1_Schwingungssystem_800x429-300x161.jpg 300w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-0-1_Schwingungssystem_800x429-768x412.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Equation 2<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8c9d992 elementor-widget elementor-widget-text-editor\" data-id=\"8c9d992\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Equation 2 can generally be formulated in the following form for <i>n<\/i> degrees of freedom:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ad072ff elementor-widget elementor-widget-image\" data-id=\"ad072ff\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"278\" height=\"56\" src=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-0-2_Schwingungssystem.png\" class=\"attachment-large size-large wp-image-9617\" alt=\"Vibration equation\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Equation 3<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-14741eb elementor-widget elementor-widget-text-editor\" data-id=\"14741eb\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>At this point it should also be clear to the vibration technology layman that<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-d325b53 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d325b53\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-1bfc296\" data-id=\"1bfc296\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-2f4f97c\" data-id=\"2f4f97c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fcacaf9 elementor-widget elementor-widget-text-editor\" data-id=\"fcacaf9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>Such real systems cannot be solved \u201cjust like that\u201d by looking at them or using technical \u201cfeeling\u201d.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-9df2449\" data-id=\"9df2449\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-6a18f9f elementor-widget elementor-widget-text-editor\" data-id=\"6a18f9f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Any \u201cquick\u201d hypothesis put forward by \u201cexperts\u201d and sometimes \u201ccreative\u201d lawyers, which is used as a \u201cquick explanation\u201d for a vibration-related cause of damage, is required<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-e883cc1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e883cc1\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-65e683c\" data-id=\"65e683c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-2b9f3b4\" data-id=\"2b9f3b4\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6d8aa44 elementor-widget elementor-widget-text-editor\" data-id=\"6d8aa44\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>of course the technical, experimental and\/or mathematical-physical verification.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-9d9ce7b\" data-id=\"9d9ce7b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-33b63d1 elementor-widget elementor-widget-heading\" data-id=\"33b63d1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Natural vibrations<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ae0642f elementor-widget__width-initial elementor-widget elementor-widget-text-editor\" data-id=\"ae0642f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>If a system is deflected from a position of equilibrium and left to its own devices, it carries out so-called \u201c <i>free oscillations<\/i> \u201d. This means that the right-hand side in equation 2 or equation 3 is set equal to zero.<\/p><p>The free oscillations are always a superposition of the various natural oscillations of the system, which in turn are characterized by the natural frequencies and the natural shapes.<\/p><p>It is therefore of <u>fundamental importance<\/u><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-e776acf elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e776acf\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-4ebfbc9\" data-id=\"4ebfbc9\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-88f20e4\" data-id=\"88f20e4\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-20ebbfc elementor-widget elementor-widget-text-editor\" data-id=\"20ebbfc\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<ul><li><em>the natural frequencies and the  <\/em><\/li><li><em>to know the associated mode shapes of an oscillatory system<\/em> ,<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-8fb7944\" data-id=\"8fb7944\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-962c724 elementor-widget__width-initial elementor-widget elementor-widget-text-editor\" data-id=\"962c724\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>when you see these vibrations<\/p><ul><li>understand,<\/li><li>explain and<\/li><li>want to influence.<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9ebc490 elementor-widget elementor-widget-heading\" data-id=\"9ebc490\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Eigenvalues \u200b\u200b\/ eigenfrequencies<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-8a75555 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8a75555\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-2281ea7\" data-id=\"2281ea7\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ea4d408 elementor-widget elementor-widget-text-editor\" data-id=\"ea4d408\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The differential equation according to equation 3 is generally solved using the approach:  <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-fce8e69\" data-id=\"fce8e69\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-95acb1d elementor-widget elementor-widget-image\" data-id=\"95acb1d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"38\" src=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-0-3_lambda.png\" class=\"attachment-thumbnail size-thumbnail wp-image-9678\" alt=\"Eigenvektor Maschinenkanzlei\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-b9256a0 elementor-widget elementor-widget-text-editor\" data-id=\"b9256a0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The following applies to the speeds and accelerations:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a44acf9 elementor-widget elementor-widget-image\" data-id=\"a44acf9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"358\" height=\"48\" src=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-0-4_lambda.png\" class=\"attachment-large size-large wp-image-9682\" alt=\"Vibrationen Maschinen\" srcset=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-0-4_lambda.png 358w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-0-4_lambda-300x40.png 300w\" sizes=\"(max-width: 358px) 100vw, 358px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Equation 4<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-992896b elementor-widget elementor-widget-text-editor\" data-id=\"992896b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>If you now insert the relationships according to equation 4 into equation 3, you generally get:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4a5ead1 elementor-widget elementor-widget-image\" data-id=\"4a5ead1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"296\" height=\"75\" src=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-0-5_lambda.png\" class=\"attachment-large size-large wp-image-9689\" alt=\"Charakteristische Gleichung Maschinenkanzlei 2\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Equation 5<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-86f4827 elementor-widget elementor-widget-text-editor\" data-id=\"86f4827\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Since the <em>e<\/em> -function can never be equal to zero, equation 5 can be reduced to the solution:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2c00312 elementor-widget elementor-widget-image\" data-id=\"2c00312\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"275\" height=\"59\" src=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-0-6_lambda.png\" class=\"attachment-large size-large wp-image-9691\" alt=\"Charakteristische Gleichung Maschinenkanzlei\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Equation 6<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6c0f122 elementor-widget elementor-widget-text-editor\" data-id=\"6c0f122\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Equation 6 is only satisfied if the expression in the brackets is identically zero or the eigenvector. Since the latter is the trivial solution, which corresponds to the static equilibrium position, but which is not of interest in the dynamic case, solutions must be found so that the expression in brackets in Equation 6 becomes identically zero.<\/p><p>This is the case when the <span style=\"font-family: Poppins, sans-serif; font-size: 17px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400;\">coefficient determinant<\/span> of this expression becomes zero according to equation 7:  <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a55c7fb elementor-widget elementor-widget-image\" data-id=\"a55c7fb\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"389\" height=\"66\" src=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-0-7_lambda.png\" class=\"attachment-large size-large wp-image-9693\" alt=\"Koeffizientendeterminante\" srcset=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-0-7_lambda.png 389w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-0-7_lambda-300x51.png 300w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Equation 7<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7a05012 elementor-widget elementor-widget-text-editor\" data-id=\"7a05012\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Something like this is for real problems<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-8489aa7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8489aa7\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-6350e45\" data-id=\"6350e45\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-1340cbe\" data-id=\"1340cbe\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9351c7c elementor-widget elementor-widget-text-editor\" data-id=\"9351c7c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>only possible with numerical methods,<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-a453124\" data-id=\"a453124\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-bdfb371 elementor-widget elementor-widget-text-editor\" data-id=\"bdfb371\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>after the <strong>physical model<\/strong> has first been created and the <strong>mathematical model<\/strong> has been derived from it.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-16f8dc4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"16f8dc4\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-be8f6fb\" data-id=\"be8f6fb\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-aa3eea0\" data-id=\"aa3eea0\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c47407a elementor-widget elementor-widget-text-editor\" data-id=\"c47407a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>This is time-consuming and requires expertise.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-a1ec739\" data-id=\"a1ec739\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-8d507a7 elementor-widget elementor-widget-text-editor\" data-id=\"8d507a7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The <em>n<\/em> zeros of the solutions according to equation 7 are the so-called eigenvalues. The natural frequencies of the vibration system can be derived from the eigenvalues.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8962b47 elementor-widget elementor-widget-heading\" data-id=\"8962b47\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Natural vibration shapes\/mode shapes<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0063bca elementor-widget elementor-widget-text-editor\" data-id=\"0063bca\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>With the solutions according to Equation 7, the natural vibration forms according to Equation 6 can now be determined. As the name suggests, they are<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-6182e2d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6182e2d\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-ea2d8b0\" data-id=\"ea2d8b0\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-b2bc547\" data-id=\"b2bc547\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4c583e2 elementor-widget elementor-widget-text-editor\" data-id=\"4c583e2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>Natural vibration forms are only defined by their shape and not their size.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-68f9292\" data-id=\"68f9292\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-1eaadd4 elementor-widget elementor-widget-text-editor\" data-id=\"1eaadd4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>This can also be generally seen from equation 6. We have a system with <i>n<\/i> degrees of freedom. We need the solution according to equation 6. To do this, the eigenvalues \u200b\u200bare first determined.<\/p><p>But now the form of the natural oscillation is of interest. This specifically means that <i>(n+1)<\/i> information is needed. However, there are only <i>n<\/i> equations available for the solution.<\/p><p>To solve this, one point of the eigenvector (eigenform) is specified and the rest is determined mathematically based on this. That is why the natural vibration form is only defined by its shape and not its size.<\/p><p>This gives you <em>n<\/em> eigenvectors.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c4554bb elementor-widget elementor-widget-heading\" data-id=\"c4554bb\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">General solution of oscillations<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-724c337 elementor-widget elementor-widget-text-editor\" data-id=\"724c337\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The following solution is therefore obtained as a general solution of the oscillation for degrees of freedom of the system as a function of time:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-22d6472 elementor-widget elementor-widget-image\" data-id=\"22d6472\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"213\" height=\"92\" src=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-0-8_lambda.png\" class=\"attachment-large size-large wp-image-9702\" alt=\"Maschinenschwingung\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Equation 8<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-99091f1 elementor-widget elementor-widget-text-editor\" data-id=\"99091f1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The coefficients <em>c_i<\/em> result from the initial conditions.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b5de7fa elementor-widget elementor-widget-heading\" data-id=\"b5de7fa\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Summary for machine vibrations and vibrations<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-378063b elementor-widget elementor-widget-text-editor\" data-id=\"378063b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Now that the very complex relationships in real vibration systems have been explained &#8211; hopefully simply and understandably &#8211; in very few words, it is clear that vibration technology is difficult and anything but understandable &#8221; <i>at first glance<\/i> &#8220;.  <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-2cb80a5a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2cb80a5a\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-inner-column elementor-element elementor-element-7d7b67a8\" data-id=\"7d7b67a8\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6a202355 elementor-widget elementor-widget-text-editor\" data-id=\"6a202355\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h4><span style=\"color: #3366ff;\">Important:<\/span><\/h4><p>Each vibration problem must be viewed individually. A solution is not possible by \u201cjust looking at it\u201d, neither when it comes to vibrations in court proceedings nor when testing vibrations or machine vibrations on behalf of the party.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-0a3c77f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0a3c77f\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-e7e2183\" data-id=\"e7e2183\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8e635cc elementor-widget elementor-widget-heading\" data-id=\"8e635cc\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Product liability for machine oscillations and vibrations  <\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a03b679 elementor-widget elementor-widget-text-editor\" data-id=\"a03b679\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The topic of product liability for product defects according to the Product Liability Act (ProdHaftG) has already been discussed in detail in the article \u201c <a href=\"https:\/\/maschinenkanzlei.de\/en\/product-liability-for-machines-product-defects\/\">Product liability for machines due to product defects<\/a> \u201d.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f12e513 elementor-widget elementor-widget-heading\" data-id=\"f12e513\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Technical product error \u201cmachine vibrations\u201d<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-889b94d elementor-widget elementor-widget-text-editor\" data-id=\"889b94d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>If a technical problem regarding vibrations in mechanical engineering and plant engineering can be confirmed, these are primarily the following technical error types:<\/p><ol><li>design errors and<\/li><li>Manufacturing defects or installation errors.<\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f05d0d2 elementor-widget elementor-widget-heading\" data-id=\"f05d0d2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Design defects in case of vibrations in court case<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-aeee5f0 elementor-widget elementor-widget-text-editor\" data-id=\"aeee5f0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The definition states that a design error only exists if technical knowledge is violated <strong>during the planning of the product<\/strong> . The<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-f9e59b4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f9e59b4\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-348b76c\" data-id=\"348b76c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-d4e8163\" data-id=\"d4e8163\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f57f6a2 elementor-widget elementor-widget-text-editor\" data-id=\"f57f6a2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>error therefore predates production<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-e2769d8\" data-id=\"e2769d8\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-2de2207 elementor-widget elementor-widget-text-editor\" data-id=\"2de2207\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>and is then also typical for the entire production series.<\/p><p>If there is actually a product series, it will be technically possible to prove such a design defect in the case of machine vibrations in a court of law as part of factual findings on a reference product.<\/p><p>It is more difficult if an individual machine has been destroyed and you then want to prove damage caused by vibrations of the machine. In such cases, as a rule  <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-d78b1da elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d78b1da\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-7266783\" data-id=\"7266783\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-ce31f8d\" data-id=\"ce31f8d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b48e361 elementor-widget elementor-widget-text-editor\" data-id=\"b48e361\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>it is no longer technically possible to provide proof.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-fc9c7f0\" data-id=\"fc9c7f0\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-f0a681a elementor-widget elementor-widget-heading\" data-id=\"f0a681a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Manufacturing defects or installation errors in the event of damage caused by vibrations<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-adfda20 elementor-widget elementor-widget-text-editor\" data-id=\"adfda20\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Manufacturing defects refer to defects that<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-b1a896a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b1a896a\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-523b944\" data-id=\"523b944\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-9abab6f\" data-id=\"9abab6f\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-72ca137 elementor-widget elementor-widget-text-editor\" data-id=\"72ca137\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>during the manufacturing process<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-7c8beb2\" data-id=\"7c8beb2\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-252ba59 elementor-widget elementor-widget-text-editor\" data-id=\"252ba59\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>appear. In the case of vibrations, resonances and oscillations in court proceedings, this usually means that<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-22d3412 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"22d3412\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-c9b0b98\" data-id=\"c9b0b98\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-e3f9841\" data-id=\"e3f9841\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8c6a6d4 elementor-widget elementor-widget-text-editor\" data-id=\"8c6a6d4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>incorrect assembly.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-6aff720\" data-id=\"6aff720\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-588eb99 elementor-widget elementor-widget-text-editor\" data-id=\"588eb99\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Incorrect assembly often leads to changes in the \u201cstiffness\u201d of the vibration system in moving machines. In the underlying equations, this always influences the stiffness matrix <em>c<\/em> according to Equation 3.<\/p><p>The problem is with individual machines that are not series products and are manufactured in small quantities:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-ffda846 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ffda846\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-3603bb0\" data-id=\"3603bb0\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-7a3a596\" data-id=\"7a3a596\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c47b9b1 elementor-widget elementor-widget-text-editor\" data-id=\"c47b9b1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>How do you want to prove this if you as a party in court proceedings have the burden of proof?<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-a33baa3\" data-id=\"a33baa3\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-c20e5b6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c20e5b6\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7cfa09c\" data-id=\"7cfa09c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c9388e8 elementor-widget elementor-widget-heading\" data-id=\"c9388e8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Examples of machine vibrations<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b5c5b04 elementor-widget elementor-widget-text-editor\" data-id=\"b5c5b04\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>There are numerous vibration examples that I could present. I have only selected two that exemplify classic situations involving machine vibrations and, in particular, vibrations in court proceedings.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-aa05292 elementor-widget elementor-widget-heading\" data-id=\"aa05292\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Vibrations of a pump<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-10fdf46 elementor-widget elementor-widget-text-editor\" data-id=\"10fdf46\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>A pump that has already been removed in Figure 2 is said to have been prone to significant vibrations after it was repaired.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cc385fb elementor-widget elementor-widget-image\" data-id=\"cc385fb\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"450\" src=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-2_Pumpenschwingungen_800x450.jpg\" class=\"attachment-large size-large wp-image-9740\" alt=\"8 pump oscillations\" srcset=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-2_Pumpenschwingungen_800x450.jpg 800w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-2_Pumpenschwingungen_800x450-300x169.jpg 300w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-2_Pumpenschwingungen_800x450-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Picture 2: Pump removed due to vibration damage.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-91639ef elementor-widget elementor-widget-text-editor\" data-id=\"91639ef\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The big problem in a situation according to Figure 2 is that neither as a party expert nor as a court expert commissioned by the court in a \u201c <em>vibration court case<\/em> \u201d is it possible to determine anything at all if the dismantling has already taken place.<\/p>\n<p>Why is that?<\/p>\n<p>The vibration behavior of structures depends very much on the boundary conditions (\u201csupports\u201d). If the oscillating masses <i>M<\/i> do not change according to Equation 3, which almost never happens with the exception of the example in Figure 1, the only influences left are<\/p>\n<ul>\n<li>the change in attenuation <i>d<\/i> ,<\/li>\n<li>the stiffness <i>c<\/i> or<\/li>\n<li>the excitation <i>f(t)<\/i> of the system remains,<\/li>\n<\/ul>\n<p>to explain damage technically. However, the crucial question in a situation according to Figure 2 is:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-3e49e47 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3e49e47\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-8edd2c4\" data-id=\"8edd2c4\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-c398b20\" data-id=\"c398b20\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-113c2cd elementor-widget elementor-widget-text-editor\" data-id=\"113c2cd\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>How is an expert supposed to find a cause if the system no longer exists in the installed and discussed or criticized state?<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-1d25899\" data-id=\"1d25899\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-0ab1979 elementor-widget elementor-widget-text-editor\" data-id=\"0ab1979\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The technical answer is very simple: <a href=\"https:\/\/maschinenkanzlei.de\/en\/destruction-of-evidence-vibrations-resonance-machine\/\">it is no longer possible!<\/a><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5f9bad3 elementor-widget elementor-widget-heading\" data-id=\"5f9bad3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Machine vibrations due to unbalance<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d891d30 elementor-widget elementor-widget-text-editor\" data-id=\"d891d30\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Figure 3 shows further damage caused by a vibration problem. There was a lot of damage, which you can hardly imagine just by looking at picture 3 in terms of its dimensions.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-319bee7 elementor-widget elementor-widget-image\" data-id=\"319bee7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"450\" src=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-3_Vibrationen-Unwucht_800x450.jpg\" class=\"attachment-large size-large wp-image-9752\" alt=\"Vibrations Imbalance\" srcset=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-3_Vibrationen-Unwucht_800x450.jpg 800w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-3_Vibrationen-Unwucht_800x450-300x169.jpg 300w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-3_Vibrationen-Unwucht_800x450-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Figure 3: Vibration damage caused by an imbalance.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-05f3562 elementor-widget elementor-widget-text-editor\" data-id=\"05f3562\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The system was permanently monitored for vibrations. After some time in operation, the operator noticed audible noises and also noticed that measured vibration paths had increased.<\/p><p>The manufacturer ignored the operator&#8217;s information because the measured vibration paths still \u201cfit\u201d the DIN standard.<\/p><p>Normally, when machines are completely destroyed, it is almost impossible to prove exactly the cause of the damage, especially in the \u201c <i>machine vibration<\/i> \u201d hypothesis.<\/p><p>However, in this case there were detailed records of the operating parameters. You could see that the system had risen in a relatively short period of time. This is always an indication of imbalance, especially with rotating structures.<\/p><p>The fact that there were detailed records of the operating parameters in this case could in principle explain the case.<\/p><p>However, the following questions are always crucial for the liability law problem to be clarified:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-a2feadd elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a2feadd\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-9b624e7\" data-id=\"9b624e7\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-ef3cfba\" data-id=\"ef3cfba\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0b4604f elementor-widget elementor-widget-text-editor\" data-id=\"0b4604f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<ol><li><em>What is or was the cause of the damage?<\/em><\/li><li><em>Who or which party is responsible for this?<\/em><\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-6c00191\" data-id=\"6c00191\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-bcf3c08 elementor-widget elementor-widget-text-editor\" data-id=\"bcf3c08\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>In the case of technical damage, including machine vibrations, the clarification of this question can keep some lawyers, insurance companies and courts busy for years in individual cases if an issue is not brought to the proverbial point.<\/p><p>Over the years, possible technical scenarios and the associated responsibilities are often legally \u201cphilosophized\u201d among those involved.<\/p><p>The important question about the technical cause of damage is usually related to the meaningful and recorded operating parameters<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-8b274a5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8b274a5\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-df0d329\" data-id=\"df0d329\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-4757e42\" data-id=\"4757e42\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-371cbf5 elementor-widget elementor-widget-text-editor\" data-id=\"371cbf5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>not yet answered.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-a3d1f3a\" data-id=\"a3d1f3a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-6de710e elementor-widget elementor-widget-text-editor\" data-id=\"6de710e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>In the present case, however, it was determined that a 160\u00b0 segment had come loose from an impeller due to a faulty weld seam. That was the reason for the imbalance. This means that this vibration damage could be resolved without going to court.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-407fe45 elementor-widget elementor-widget-heading\" data-id=\"407fe45\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Vibrations in the court proceedings<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f1d76ed elementor-widget elementor-widget-text-editor\" data-id=\"f1d76ed\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>A lawsuit claimed that \u201cnoticeable vibrations\u201d were detected on a generator. The vibration measurement in <u>one point<\/u> was decisive for the lawsuit regarding machine vibrations.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-384d58c elementor-widget elementor-widget-image\" data-id=\"384d58c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"450\" src=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-4_Schwingungsmessung_800x450.jpg\" class=\"attachment-large size-large wp-image-9760\" alt=\"8 Schwingungsmessung\" srcset=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-4_Schwingungsmessung_800x450.jpg 800w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-4_Schwingungsmessung_800x450-300x169.jpg 300w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-4_Schwingungsmessung_800x450-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Figure 4: Vibration measurement of vibrations of a machine at one point.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7d2512a elementor-widget elementor-widget-text-editor\" data-id=\"7d2512a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Of course it is possible to measure machine vibrations at one point. For example, if you make technical changes to the system and carry out comparison measurements at one and the same point, you will most likely be able to detect changes in the vibration response when comparing the measurement results.<\/p><p>For comparison purposes it is \u201cok\u201d from the technical category. For absolute statements, selective measurements on structures are risky because essential information can be lost.<\/p><p>I refer to section 6.1.1.1 \u201cNodal lines\u201d. If you measure points along a nodal line of a form of natural oscillation that dominates the excitation, you are measuring \u201csomething\u201d or, theoretically, nothing at all. In any case, in such a case you are not measuring anything technically meaningful.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-144380e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"144380e\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-243c749\" data-id=\"243c749\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7e5c4bb elementor-widget elementor-widget-heading\" data-id=\"7e5c4bb\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Machine vibrations in court evidence<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6992e90 elementor-widget elementor-widget-text-editor\" data-id=\"6992e90\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>A judicial order for evidence is a judicial order issued as part of a legal proceeding and aimed at regulating the taking of evidence. The evidentiary order serves to ensure that all relevant facts and circumstances can be identified and assessed in the course of a legal dispute.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b144ab2 elementor-widget elementor-widget-image\" data-id=\"b144ab2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"279\" src=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-4_Frequenzspektrum_800x4xx.jpg\" class=\"attachment-large size-large wp-image-9763\" alt=\"Frequenzspektrum\" srcset=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-4_Frequenzspektrum_800x4xx.jpg 800w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-4_Frequenzspektrum_800x4xx-300x105.jpg 300w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-4_Frequenzspektrum_800x4xx-768x268.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Figure 3: Frequency spectrum.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-50dd352 elementor-widget elementor-widget-text-editor\" data-id=\"50dd352\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><a data-wpil=\"url\" href=\"https:\/\/maschinenkanzlei.de\/en\/expert-machines-sv-frank-flammer\/\">Court experts<\/a> are bound by the evidence decision. The questions asked there must be answered accordingly.<\/p><p>The courts often incorporate the parties&#8217; formulations from the lawyers&#8217; pleadings more or less exactly into the court&#8217;s evidentiary decision. It is also understandable because, after all, lawyers are experts in the law and not in every single discipline from which a problem arises on which the court has to make a decision in the context of the lawsuit.<\/p><p>This regularly leads to extremely imprecise technical questions in the area of \u200b\u200bvibrations in court proceedings. The following two examples should give an impression. I could give a number of examples here.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-72122c4 elementor-widget elementor-widget-heading\" data-id=\"72122c4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Example 1 for judicial evidence in the case of machine vibrations<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f7166d9 elementor-widget elementor-widget-text-editor\" data-id=\"f7166d9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Figure 4 shows the evidentiary decision for a vibration case in court.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4d71258 elementor-widget elementor-widget-image\" data-id=\"4d71258\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"796\" height=\"257\" src=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-5-1_BW-1.jpg\" class=\"attachment-large size-large wp-image-9773\" alt=\"Order of evidence Court Machine Law Firm\" srcset=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-5-1_BW-1.jpg 796w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-5-1_BW-1-300x97.jpg 300w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-5-1_BW-1-768x248.jpg 768w\" sizes=\"(max-width: 796px) 100vw, 796px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Figure 4: 1. Example of an evidentiary decision on machine vibrations.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4629445 elementor-widget elementor-widget-text-editor\" data-id=\"4629445\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>In the example shown in Figure 4, the professional expert in the field of machine vibration immediately faces technical questions:<\/p><ol><li>What are \u201cnoticeable vibrations\u201d?<\/li><li>How were these machine vibrations determined?<\/li><li>Where were these vibrations detected or where should the vibrations be detected in the legal proceedings?<\/li><\/ol><p>In addition, such an evidentiary decision raises the question of how a court expert is supposed to determine what any employees may have said in the meantime. Examining witnesses is the task of the responsible court. Court experts are not allowed to examine witnesses. Rather, they are experts in their specific field and the court&#8217;s helpers in this field.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3afa0aa elementor-widget elementor-widget-heading\" data-id=\"3afa0aa\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Example 2 for court decisions regarding vibrations<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3f72ee3 elementor-widget elementor-widget-text-editor\" data-id=\"3f72ee3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The example in Figure 5 shows that the discharge screws are no longer installed in the system being assessed at the time of the legal proceedings.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-31ae055 elementor-widget elementor-widget-image\" data-id=\"31ae055\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"145\" src=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-5-2_BW.jpg\" class=\"attachment-large size-large wp-image-9783\" alt=\"8-5-2 Evidence Decision Machine Vibrations\" srcset=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-5-2_BW.jpg 800w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-5-2_BW-300x54.jpg 300w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-5-2_BW-768x139.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Figure 5: 2. Example of an evidentiary decision on vibrations in court proceedings.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-de81a6d elementor-widget elementor-widget-text-editor\" data-id=\"de81a6d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>A judge has no chance of recognizing that something like this can no longer be checked in the case of vibrations in machines.<\/p><p>When it comes to such evidentiary decisions, it is always unclear to me why parties enter into a legal dispute under such technical conditions. There must be competent technical experts on the party&#8217;s side who should give the party lawyers appropriate technical advice. The crucial question for the forensic expert in a case according to Figure 5 is:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-3c03ef1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3c03ef1\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-8b79b63\" data-id=\"8b79b63\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-a14ac62\" data-id=\"a14ac62\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3ac8ce2 elementor-widget elementor-widget-text-editor\" data-id=\"3ac8ce2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>How should this question be answered? It&#8217;s not working.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-1230431\" data-id=\"1230431\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6ac0476 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6ac0476\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-957a3e3\" data-id=\"957a3e3\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e7dde38 elementor-widget elementor-widget-heading\" data-id=\"e7dde38\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Why is the vibration system so important?<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-06edcbc elementor-widget elementor-widget-text-editor\" data-id=\"06edcbc\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>It is of fundamental importance<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-dc79d63 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"dc79d63\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-0f55342\" data-id=\"0f55342\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-dc295e1\" data-id=\"dc295e1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a9b5fef elementor-widget elementor-widget-text-editor\" data-id=\"a9b5fef\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<ul><li><em>the natural frequencies and<\/em><\/li><li><em>the natural vibration forms<\/em><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-01750ee\" data-id=\"01750ee\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-09fada8 elementor-widget elementor-widget-text-editor\" data-id=\"09fada8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>to know or determine the vibration system in machine vibrations. An expert must therefore understand the vibration system in order to enable substantiated findings regarding vibrations in court proceedings.<\/p><p>Regardless of the absolute magnitude of the system&#8217;s excitations (\u201c <i>excitations<\/i> \u201d) and dampings, knowledge of the essential natural frequencies and mode shapes is very helpful in order to be able to evaluate the dynamic behavior.<\/p><p>There are measurement methods that can be used to represent the natural vibration patterns of real structures.<\/p><p>If you have the design data available and compare it with the structure implemented in reality, you can examine real structures relatively easily &#8211; albeit with a lot of time &#8211; using suitable software.<\/p><p>Depending on the discretization of the structure, the analysis results, for example using the finite element method (FEM), are very precise with regard to the natural vibration forms. The natural frequencies then determined are:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-39ed991 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"39ed991\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-d92194f\" data-id=\"d92194f\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-15ba89e\" data-id=\"15ba89e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7113e37 elementor-widget elementor-widget-text-editor\" data-id=\"7113e37\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>there are always sometimes clear deviations from reality.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-22177e8\" data-id=\"22177e8\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-67d524b elementor-widget elementor-widget-text-editor\" data-id=\"67d524b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>However, knowledge of the natural vibration forms is essential because you then know which \u201cshape\u201d you need to shift towards the desired frequency ranges through \u201cwhich\u201d interventions in the structure in order to avoid undesirable effects.<\/p><p>The following must be taken into account:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-bf1d82b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bf1d82b\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-c486669\" data-id=\"c486669\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-7a36ee0\" data-id=\"7a36ee0\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4a887de elementor-widget elementor-widget-text-editor\" data-id=\"4a887de\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>No expert can do something like this just by looking at it<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-1233f04\" data-id=\"1233f04\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-ebd2884 elementor-widget elementor-widget-text-editor\" data-id=\"ebd2884\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>and especially not if<\/p><ul><li>the damage has already happened and<\/li><li>the structures dismantled or<\/li><li>are destroyed.<\/li><\/ul><p>In all of these cases, essential technical information was lost. This is with vibrations in court proceedings<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-859f7cb elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"859f7cb\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-faebce8\" data-id=\"faebce8\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-5527645\" data-id=\"5527645\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ffada6a elementor-widget elementor-widget-text-editor\" data-id=\"ffada6a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>always associated with a disadvantage for the party responsible for providing evidence.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-ec29b28\" data-id=\"ec29b28\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-0eef64e elementor-widget elementor-widget-text-editor\" data-id=\"0eef64e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The following simple example will illustrate why the vibration system is so important.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c3e905b elementor-widget elementor-widget-heading\" data-id=\"c3e905b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Influence of boundary conditions on vibrations using a simple example<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-071c282 elementor-widget elementor-widget-text-editor\" data-id=\"071c282\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>In Figure 6 you can see a top view of two simple rectangular plates that were depicted in a so-called shell model in an FEM analysis.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b2ec47a elementor-widget elementor-widget-image\" data-id=\"b2ec47a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"327\" src=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-6-1-2_Analysemodell_800x.jpg\" class=\"attachment-large size-large wp-image-9785\" alt=\"8 analysis model\" srcset=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-6-1-2_Analysemodell_800x.jpg 800w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-6-1-2_Analysemodell_800x-300x123.jpg 300w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-6-1-2_Analysemodell_800x-768x314.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Figure 6: Model with boundary condition 1 \/ boundary condition 2.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-80e9433 elementor-widget elementor-widget-text-editor\" data-id=\"80e9433\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>With the label \u201c1\u201d, \u201cleft\u201d in Figure 6, the two light blue edges are completely blocked (\u201cboundary condition 1\u201d in Table 1). Shifts are excluded along these blue edges.<\/p><p>With the label \u201c2\u201d, \u201cright\u201d in Figure 6, only the red edges are completely blocked. Shifts are possible \u201cbottom right\u201d (\u201cboundary condition 2\u201d in Table 1).<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6280564 elementor-widget elementor-widget-heading\" data-id=\"6280564\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Natural vibration forms (\u201cmodes\u201d)<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6c0b17e elementor-widget elementor-widget-text-editor\" data-id=\"6c0b17e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Figure 7 shows the comparison of the first mode shape. In case &#8220;1&#8221; with both completely blocked edges, the classic antinode results, which runs exactly in the middle if there is symmetry.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a7e328e elementor-widget elementor-widget-image\" data-id=\"a7e328e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"254\" src=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-6-2_Modes_800x.jpg\" class=\"attachment-large size-large wp-image-9787\" alt=\"8 natural vibration modes\" srcset=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-6-2_Modes_800x.jpg 800w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-6-2_Modes_800x-300x95.jpg 300w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-6-2_Modes_800x-768x244.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Figure 7: Mode 1 \u2013 RB1\/RB2 - 3.47 Hz\/1.40 Hz.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-139e437 elementor-widget elementor-widget-text-editor\" data-id=\"139e437\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>In case \u201c2\u201d only the exposed edge area vibrates. The associated frequency is a full 2 \u200b\u200bHz lower than in case \u201c1\u201d with clamping over the entire edge.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-de30136 elementor-widget elementor-widget-heading\" data-id=\"de30136\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h5 class=\"elementor-heading-title elementor-size-default\">Nodal lines for oscillations, vibrations, resonances<\/h5>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3ef6c0f elementor-widget elementor-widget-text-editor\" data-id=\"3ef6c0f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Figure 8 also shows significant differences in the natural vibration shape and of course in the natural frequency. In both cases you can see the so-called <i>nodal lines<\/i> .<\/p><p>In two-dimensional structures, nodal lines mean that natural vibration forms along these lines<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-2b67de5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2b67de5\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-263350d\" data-id=\"263350d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-ccfad98\" data-id=\"ccfad98\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0cfc2dc elementor-widget elementor-widget-text-editor\" data-id=\"0cfc2dc\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>are at rest \u201cdespite vibration\u201d and remain so.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-e0fbc24\" data-id=\"e0fbc24\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-d3db946 elementor-widget elementor-widget-text-editor\" data-id=\"d3db946\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>You can see in the left part of Figure 8 (\u201cBoundary condition 1\u201d) that the expected symmetry is present here. In the case with the edge only partially clamped, a natural vibration form results, which is a combination of the vibration antinode present in the case of symmetry according to Figure 7 (\u201cleft\u201d) and the vibration behavior according to Figure 7 (\u201cright\u201d).<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d58d4ca elementor-widget elementor-widget-image\" data-id=\"d58d4ca\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"242\" src=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-6-3_Knotenlinen_800x.jpg\" class=\"attachment-large size-large wp-image-9789\" alt=\"Node Line Vibration Machine Office\" srcset=\"https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-6-3_Knotenlinen_800x.jpg 800w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-6-3_Knotenlinen_800x-300x91.jpg 300w, https:\/\/maschinenkanzlei.de\/wp-content\/uploads\/2023\/12\/8-6-3_Knotenlinen_800x-768x232.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Figure 8: Mode 2 \u2013 RB1\/RB2 - 4.11 Hz\/3.41 Hz.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-9ba4a86 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9ba4a86\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-7104c3e\" data-id=\"7104c3e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-df9ae36\" data-id=\"df9ae36\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-aa6ceb7 elementor-widget__width-initial elementor-widget elementor-widget-text-editor\" data-id=\"aa6ceb7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"text-align: center;\">\n<table id=\"tablepress-38\" class=\"tablepress tablepress-id-38\">\n<thead>\n<tr class=\"row-1\">\n\t<th class=\"column-1\">Mode<\/th><th class=\"column-2\">&#8220;1&#8221;<\/th><th class=\"column-3\">&#8220;2&#8221;<\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"row-striping row-hover\">\n<tr class=\"row-2\">\n\t<td class=\"column-1\">1<\/td><td class=\"column-2\">3,47 Hz<\/td><td class=\"column-3\">1,40 Hz<\/td>\n<\/tr>\n<tr class=\"row-3\">\n\t<td class=\"column-1\">2<\/td><td class=\"column-2\">4,11 Hz<\/td><td class=\"column-3\">3,41 Hz<\/td>\n<\/tr>\n<tr class=\"row-4\">\n\t<td class=\"column-1\">3<\/td><td class=\"column-2\">6,73 Hz<\/td><td class=\"column-3\">4,45 Hz<\/td>\n<\/tr>\n<tr class=\"row-5\">\n\t<td class=\"column-1\">4<\/td><td class=\"column-2\">9,58 Hz<\/td><td class=\"column-3\">5,6 Hz<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-38 from cache --><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f125fc0 elementor-widget elementor-widget-text-editor\" data-id=\"f125fc0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"text-align: center;\">Table 1: Influence of boundary conditions.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-8cb73be\" data-id=\"8cb73be\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-d930a81 elementor-widget elementor-widget-text-editor\" data-id=\"d930a81\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>If you now look at the determined natural frequencies 3 and 4 according to Table 1, you can also see clear differences here.<\/p><p>This example is intended to make it clear that boundary conditions such as:<\/p><ul><li>connections,<\/li><li>storage,<\/li><li>movement options, etc.<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-cf6049d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"cf6049d\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-d2f87f0\" data-id=\"d2f87f0\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-5a28c28\" data-id=\"5a28c28\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7e581fe elementor-widget elementor-widget-text-editor\" data-id=\"7e581fe\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>significantly influence the vibration behavior of structures.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-97f7016\" data-id=\"97f7016\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-7e2eb33 elementor-widget elementor-widget-text-editor\" data-id=\"7e2eb33\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>This change refers to the<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-e99e567 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e99e567\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-315152b\" data-id=\"315152b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-ec693c6\" data-id=\"ec693c6\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ed06e46 elementor-widget elementor-widget-text-editor\" data-id=\"ed06e46\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>Natural frequencies and the natural vibration forms (\u201cmodes\u201d) associated with these natural frequencies.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-de49d5b\" data-id=\"de49d5b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-9c4695c elementor-widget elementor-widget-text-editor\" data-id=\"9c4695c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>This is intended to make it clear again for the layperson at this point that one must know<\/p><ul><li>what you are looking for and most importantly<\/li><li>at what frequency,<\/li><\/ul><p>so that technical conclusions can be drawn about events and &#8211; ideally &#8211; avoided in the future. It follows:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-bf8274b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bf8274b\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-e99d443\" data-id=\"e99d443\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-e48d936\" data-id=\"e48d936\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d0b299b elementor-widget elementor-widget-text-editor\" data-id=\"d0b299b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>Vibration problems such as machine vibrations are therefore a technically very demanding area of \u200b\u200bresponsibility for specialists.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-2ef0fe3\" data-id=\"2ef0fe3\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4ff6f74 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4ff6f74\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-68192df\" data-id=\"68192df\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8dc8b9b elementor-widget elementor-widget-heading\" data-id=\"8dc8b9b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Technical recommendations<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d73bbe9 elementor-widget elementor-widget-text-editor\" data-id=\"d73bbe9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The explanations are just a very short excursion into the fascinating area of \u200b\u200bvibration technology and vibration-related problems in machines and systems in mechanical engineering.<\/p><p>I strongly recommend that parties carefully consider the technical aspects or seek advice from vibration experts about the extent to which there may be a vibration problem. After that it is<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-c188c7b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c188c7b\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-b7a6d9c\" data-id=\"b7a6d9c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-ab76ebb\" data-id=\"ab76ebb\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-553a156 elementor-widget elementor-widget-text-editor\" data-id=\"553a156\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>It is important to check whether and, if so, how this can be proven in a legal dispute.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-d66e5be\" data-id=\"d66e5be\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-c1cbab2 elementor-widget elementor-widget-text-editor\" data-id=\"c1cbab2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>If a party with a technical problem in the area of \u200b\u200bmachine vibrations wants to initiate an independent evidentiary procedure or even file a lawsuit in court, the party should be sure that evidence can also be provided in the legal dispute.<\/p><p>It is always quite easy for a lawyer to offer \u201c <em>evidence: expert opinion<\/em> \u201d in a lawsuit or in independent evidence proceedings.<\/p><p>However, this doesn&#8217;t help if a forensic expert can no longer determine anything, because<\/p><ul><li>the vibration system is destroyed or<\/li><li>was changed until the on-site court hearing.<\/li><\/ul><p>If a party has come to the technical conclusion internally or even with the help of a technically good party expert that an alleged problem with machine vibrations can also be proven in a legal dispute, I can only recommend that relevant questions be included in the evidentiary decision<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-e091dde elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e091dde\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-676b3d4\" data-id=\"676b3d4\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-1b76073\" data-id=\"1b76073\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6512583 elementor-widget elementor-widget-text-editor\" data-id=\"6512583\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>to be formulated in <u>a technically<\/u> precise manner<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-f893db0\" data-id=\"f893db0\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-c781295 elementor-widget elementor-widget-text-editor\" data-id=\"c781295\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>and this in the case of \u201c <em>vibrations in court proceedings<\/em> \u201d<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-87b1a99 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"87b1a99\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-38d8846\" data-id=\"38d8846\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-ccd23ee\" data-id=\"ccd23ee\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-950ac4c elementor-widget elementor-widget-text-editor\" data-id=\"950ac4c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>not lawyers from your own party<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-82673db\" data-id=\"82673db\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-d0a7bb1 elementor-widget elementor-widget-text-editor\" data-id=\"d0a7bb1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>to leave.<\/p><p>This is not a distrust of the legal profession. I met fantastic lawyers. It is always a pleasure to work with legal experts on tricky technical cases at a high level. But lawyers are experts in the law.<\/p><p>Based on the above, it should be clear that vibrations are a very difficult technical topic. This is particularly true when it is necessary to prove something in a legal dispute over \u201cmachine vibrations\u201d.<\/p><p>Lawyers cannot have this technical know-how. That&#8217;s why excellent <a data-wpil=\"url\" href=\"https:\/\/maschinenkanzlei.de\/en\/expert-machines-sv-frank-flammer\/\">professional advice<\/a> is always necessary on the party&#8217;s side when there are oscillations in court proceedings. Basically I recommend:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-cfab9b8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"cfab9b8\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-039c8b6\" data-id=\"039c8b6\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-71bfb97\" data-id=\"71bfb97\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-22aa88a elementor-widget elementor-widget-text-editor\" data-id=\"22aa88a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>As a party, think carefully about whether you want to take a high risk in a legal dispute in the case of machine vibrations.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-eade537\" data-id=\"eade537\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-304c855 elementor-widget elementor-widget-text-editor\" data-id=\"304c855\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Due to the fact that the problem has already been \u201csettled\u201d in almost all cases, oscillations in court proceedings can almost never be reliably determined and explained subsequently by court experts. There will always be unexplained aspects. This is always helpful in legal disputes for the party not required to provide evidence.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c6e9593 elementor-widget elementor-widget-heading\" data-id=\"c6e9593\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Litigation risk for parties in the event of fluctuations in the court proceedings<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-052d138 elementor-widget elementor-widget-text-editor\" data-id=\"052d138\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>In principle, in a legal dispute there is a risk that court experts will comment on technical questions in which they simply overestimate their own competence.<\/p><p>Particularly when it comes to machine vibrations, absolute know-how in terms of oscillations, vibrations, resonances and structural mechanics as well as structural dynamics is necessary. When it comes to machine vibrations, no court expert or technical expert is able to answer \u201cseemingly\u201d simple questions from the parties\u2019 lawyers on an ad hoc basis, for example in court hearings.<\/p><p>This is also easy to explain: if you just look at the general representation of a system of differential equations according to Equation 2, it should be clear to even the layperson that it is completely utopian to be able to predict the influence of any parameter changes \u201cjust like that\u201d.<\/p><p>So be on your guard if a technical expert in this specific area of \u200b\u200bmachine vibration tells you in court proceedings or on the party&#8217;s side:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-15105d0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"15105d0\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-0be65bb\" data-id=\"0be65bb\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-189a220\" data-id=\"189a220\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-93770d0 elementor-widget elementor-widget-text-editor\" data-id=\"93770d0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>\u201cBased on experience, I can tell you that\u2026.\u201d<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-8057aa1\" data-id=\"8057aa1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-1f99b36 elementor-widget elementor-widget-text-editor\" data-id=\"1f99b36\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>In principle, in a legal dispute there is a risk that court experts will comment on technical questions in which they simply overestimate their own competence.<\/p><p>Particularly when it comes to machine vibrations, absolute know-how in terms of oscillations, vibrations, resonances and structural mechanics as well as structural dynamics is necessary. No technical expert or technical expert is able to answer seemingly simple questions on an ad hoc basis from the parties&#8217; lawyers, for example in court hearings.<\/p><p>This is also easy to explain: if you just look at the general representation of a system of differential equations according to Equation 2, it should be clear to even the layperson that it is completely utopian to be able to predict the influence of any parameter changes \u201cjust like that\u201d.<\/p><p>So be on your guard if a technical expert in this specific area of \u200b\u200bmachine vibration tells you in court proceedings or on the party&#8217;s side:  <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-2b0d080 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2b0d080\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-c44359b\" data-id=\"c44359b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-1943f5e\" data-id=\"1943f5e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fea3564 elementor-widget elementor-widget-text-editor\" data-id=\"fea3564\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>\u201cBased on experience, I can tell you that\u2026.\u201d<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-8d6be4d\" data-id=\"8d6be4d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-75d1588 elementor-widget elementor-widget-text-editor\" data-id=\"75d1588\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>I can tell you that<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-f1fb3ab elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f1fb3ab\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-b6c94f4\" data-id=\"b6c94f4\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-8631618\" data-id=\"8631618\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-525b1ec elementor-widget elementor-widget-text-editor\" data-id=\"525b1ec\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>is definitely a misconception, coupled with overestimation of oneself<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-9cecb09\" data-id=\"9cecb09\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-54b134b elementor-widget elementor-widget-text-editor\" data-id=\"54b134b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>and with machine vibrations, with vibrations in general and of course also with vibrations in court proceedings<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-3c1fa5d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3c1fa5d\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-594b0d3\" data-id=\"594b0d3\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-2058aa8\" data-id=\"2058aa8\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fa63cd0 elementor-widget elementor-widget-text-editor\" data-id=\"fa63cd0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>doesn&#8217;t work.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-d0aa7e1\" data-id=\"d0aa7e1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-f5136e1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f5136e1\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4971238\" data-id=\"4971238\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-bb74320 elementor-widget elementor-widget-heading\" data-id=\"bb74320\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Conclusion and final thoughts<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9b9fa8d elementor-widget elementor-widget-text-editor\" data-id=\"9b9fa8d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Machine vibrations can lead to legal disputes if they are viewed as the cause of product defects (product liability), damage or health problems. In all machine vibration cases, the burden of proof is the crucial issue when resolving vibration issues in court proceedings.<\/p><p>Most often in reality there are problems with machine vibrations<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-872d932 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"872d932\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-2af7b74\" data-id=\"2af7b74\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-16c5957\" data-id=\"16c5957\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-54513ad elementor-widget elementor-widget-text-editor\" data-id=\"54513ad\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>Essential technical findings in the case of vibrations are no longer possible in court proceedings,<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-25c1f6c\" data-id=\"25c1f6c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-9b630fa elementor-widget elementor-widget-text-editor\" data-id=\"9b630fa\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>because in the meantime<\/p><ul><li>the oscillating system changes or<\/li><li>the machine was destroyed by the damage or something else<\/li><li>essential information relating to vibrations has been destroyed.<\/li><\/ul><p>What is irritating is that in general many people from both the technical and non-technical and legal sectors have great respect for \u201cstatics\u201d. This is possibly because sooner or later you will be confronted with statics in your private life, for example when building your own home, and you will ultimately be satisfied when the statics have been checked. However, in the physical sense, statics is the waste product of vibration technology or dynamics. If you delete the accelerations and velocities from a differential equation system according to Equation 2 or Equation 3, which characterizes the vibration behavior, you arrive at the static solution.<\/p><p>In particular, in <a href=\"https:\/\/maschinenkanzlei.de\/en\/evidence-decision-zpo-machine-expert\/\" data-wpil-monitor-id=\"148\">legal disputes<\/a> it is documented that one thing did not usually occur between the parties:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-76d55fb elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"76d55fb\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-b7e0f3a\" data-id=\"b7e0f3a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-8d08349\" data-id=\"8d08349\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7ae98e8 elementor-widget elementor-widget-text-editor\" data-id=\"7ae98e8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>The definition of clear technical requirements on the one hand and the associated detailed understanding of the vibration problem and its technical solution on the other.  <\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-48d0217\" data-id=\"48d0217\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-fdaf00f elementor-widget elementor-widget-text-editor\" data-id=\"fdaf00f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>It is often interesting to find out in the legal dispute and after knowing the file situation how little technical information the parties use to make vibration-related promises or \u201cbelieve\u201d that they can technically solve problems with machine vibrations.<\/p><p>However, vibration technology is usually extremely complicated, very time-consuming and is <span style=\"font-family: Poppins, sans-serif; font-size: 17px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; color: var( --e-global-color-text ); letter-spacing: var( --e-global-typography-1b69a38-letter-spacing ); word-spacing: var( --e-global-typography-1b69a38-word-spacing ); background-color: var( --e-global-color-6da8ab0 );\">understandably<\/span> overlooked by the lawyers involved<span style=\"font-family: Poppins, sans-serif; font-size: 17px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; color: var( --e-global-color-text ); letter-spacing: var( --e-global-typography-1b69a38-letter-spacing ); word-spacing: var( --e-global-typography-1b69a38-word-spacing ); background-color: var( --e-global-color-6da8ab0 );\"> <\/span><span style=\"font-size: 17px; color: var( --e-global-color-text ); letter-spacing: var( --e-global-typography-1b69a38-letter-spacing ); word-spacing: var( --e-global-typography-1b69a38-word-spacing ); background-color: var( --e-global-color-6da8ab0 );\">of course completely underestimated.<\/span><\/p><p>Of course, publicly appointed and sworn experts provide advice as <a href=\"https:\/\/tes-online.org\/frank-flammer-tes-sachverstaendige\/\" target=\"_blank\" rel=\"noopener\">specialists<\/a> and technical experts and can develop solutions for complex vibration problems. However, this can only be done on behalf of the party for a reasonable fee.<\/p><p>If there are fluctuations in the legal proceedings, the court expert can only explain<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-66f2c68 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"66f2c68\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-5bd89c7\" data-id=\"5bd89c7\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-c50d5bf\" data-id=\"c50d5bf\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-627fb5f elementor-widget elementor-widget-text-editor\" data-id=\"627fb5f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>where mistakes may have been made,<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-6726438\" data-id=\"6726438\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-c783faa elementor-widget elementor-widget-text-editor\" data-id=\"c783faa\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>and who is responsible for it from a technical point of view<\/p><ul><li>bears technical responsibility and<\/li><li>what effects possible technical errors had on the agreed service.<\/li><\/ul><p>Such an approach is usually possible in the event of oscillations in court proceedings, but \u2013 understandably \u2013 does not provide a technical solution.<\/p><p>Problems from the areas of structural mechanics and structural dynamics with questions about cracks, fractures, structural failure, fatigue strength, vibration technology and machine vibrations are a case for technical specialists in all areas of mechanical and plant engineering, of which there are relatively few on the market. What is essential in this subject area is:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-e4483d4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e4483d4\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-adfdf28\" data-id=\"adfdf28\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-13f19cb\" data-id=\"13f19cb\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-07681b7 elementor-widget elementor-widget-text-editor\" data-id=\"07681b7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>Quick solutions will almost certainly lead to technical and sooner or later legal problems.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-e835b1f\" data-id=\"e835b1f\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Vibrations in mechanical engineering are always a topic in court decisions and are&#8230; problematic.<\/p>\n","protected":false},"author":1,"featured_media":9589,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ocean_post_layout":"full-screen","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"0","ocean_second_sidebar":"0","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"0","ocean_custom_header_template":"0","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"0","ocean_menu_typo_font_family":"0","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"on","ocean_disable_heading":"default","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"default","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":"0","osh_disable_topbar_sticky":"default","osh_disable_header_sticky":"default","osh_sticky_header_style":"default","osh_sticky_header_effect":"","osh_custom_sticky_logo":0,"osh_custom_retina_sticky_logo":0,"osh_custom_sticky_logo_height":0,"osh_background_color":"","osh_links_color":"","osh_links_hover_color":"","osh_links_active_color":"","osh_links_bg_color":"","osh_links_hover_bg_color":"","osh_links_active_bg_color":"","osh_menu_social_links_color":"","osh_menu_social_hover_links_color":"","ocean_post_oembed":"","ocean_post_self_hosted_media":"","ocean_post_video_embed":"","ocean_link_format":"","ocean_link_format_target":"self","ocean_quote_format":"","ocean_quote_format_link":"post","ocean_gallery_link_images":"on","ocean_gallery_id":[],"footnotes":""},"categories":[52,47],"tags":[],"class_list":["post-9894","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gerichtsgutachten","category-praxiswissen","entry","has-media"],"_links":{"self":[{"href":"https:\/\/maschinenkanzlei.de\/en\/wp-json\/wp\/v2\/posts\/9894","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/maschinenkanzlei.de\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/maschinenkanzlei.de\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/maschinenkanzlei.de\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/maschinenkanzlei.de\/en\/wp-json\/wp\/v2\/comments?post=9894"}],"version-history":[{"count":3,"href":"https:\/\/maschinenkanzlei.de\/en\/wp-json\/wp\/v2\/posts\/9894\/revisions"}],"predecessor-version":[{"id":14161,"href":"https:\/\/maschinenkanzlei.de\/en\/wp-json\/wp\/v2\/posts\/9894\/revisions\/14161"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/maschinenkanzlei.de\/en\/wp-json\/wp\/v2\/media\/9589"}],"wp:attachment":[{"href":"https:\/\/maschinenkanzlei.de\/en\/wp-json\/w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