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<a accesskey="h" href="./index.html"> UP </a>
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@@ -280,20 +30,20 @@ for the JavaScript code in this tag.
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#org93dde66">1. Type of Model</a></li>
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<li><a href="#orgfd7d140">2. <span class="todo TODO">TODO</span> Extract Physical Matrices</a></li>
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<li><a href="#orgdaaea25">3. Some notes about constraining the number of degrees of freedom</a></li>
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<li><a href="#org2a87d8f">1. Type of Model</a></li>
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<li><a href="#orgdb0ed87">2. Extract Physical Matrices</a></li>
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<li><a href="#orgcc897f4">3. Some notes about constraining the number of degrees of freedom</a></li>
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</ul>
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<div id="outline-container-org93dde66" class="outline-2">
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<h2 id="org93dde66"><span class="section-number-2">1</span> Type of Model</h2>
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<div id="outline-container-org2a87d8f" class="outline-2">
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<h2 id="org2a87d8f"><span class="section-number-2">1</span> Type of Model</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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The model that we want to obtain is a <b>multi-body model</b>.
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It is composed of several <b>solid bodies connected with springs and dampers</b>.
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The solid bodies are represented with different colors on figure <a href="#org4703119">1</a>.
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The solid bodies are represented with different colors on figure <a href="#orga016307">1</a>.
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</p>
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<p>
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@@ -308,7 +58,7 @@ In the simscape model, the solid bodies are:
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</ul>
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<div id="org4703119" class="figure">
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<div id="orga016307" class="figure">
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<p><img src="img/nass_solidworks.png" alt="nass_solidworks.png" width="800px" />
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</p>
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<p><span class="figure-number">Figure 1: </span>CAD view of the ID31 Micro-Station</p>
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@@ -325,15 +75,15 @@ The modal identification done here will thus permit us to determine <b>which DOF
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</div>
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</div>
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<div id="outline-container-orgfd7d140" class="outline-2">
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<h2 id="orgfd7d140"><span class="section-number-2">2</span> <span class="todo TODO">TODO</span> Extract Physical Matrices</h2>
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<div id="outline-container-orgdb0ed87" class="outline-2">
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<h2 id="orgdb0ed87"><span class="section-number-2">2</span> Extract Physical Matrices</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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<a class='org-ref-reference' href="#wang11_extrac_real_modes_physic_matric">wang11_extrac_real_modes_physic_matric</a>
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(<a href="#citeproc_bib_item_2">Wang, Zhang, and Tee 2011</a>)
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</p>
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<p>
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Let's recall that:
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Let’s recall that:
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\[ \Lambda = \begin{bmatrix}
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s_1 & & 0 \\
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& \ddots & \\
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@@ -361,14 +111,14 @@ Let's recall that:
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a = modal_a_M;
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lambda = eigen_val_M;
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M = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span><span class="org-type">*</span>inv<span class="org-rainbow-delimiters-depth-1">(</span>real<span class="org-rainbow-delimiters-depth-2">(</span>psi<span class="org-type">*</span>inv<span class="org-rainbow-delimiters-depth-3">(</span>a<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">*</span>lambda<span class="org-type">*</span>psi'<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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C = <span class="org-type">-</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>M<span class="org-type">*</span>real<span class="org-rainbow-delimiters-depth-1">(</span>psi<span class="org-type">*</span>inv<span class="org-rainbow-delimiters-depth-2">(</span>a<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">*</span>lambda<span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>inv<span class="org-rainbow-delimiters-depth-2">(</span>a<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">*</span>psi'<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span>M;
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K = <span class="org-type">-</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span><span class="org-type">*</span>inv<span class="org-rainbow-delimiters-depth-1">(</span>real<span class="org-rainbow-delimiters-depth-2">(</span>psi<span class="org-type">*</span>inv<span class="org-rainbow-delimiters-depth-3">(</span>lambda<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">*</span>inv<span class="org-rainbow-delimiters-depth-3">(</span>a<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">*</span>psi'<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
M = 0.5<span class="org-type">*</span>inv(real(psi<span class="org-type">*</span>inv(a)<span class="org-type">*</span>lambda<span class="org-type">*</span>psi<span class="org-type">'</span>));
|
||||
C = <span class="org-type">-</span>2<span class="org-type">*</span>M<span class="org-type">*</span>real(psi<span class="org-type">*</span>inv(a)<span class="org-type">*</span>lambda<span class="org-type">^</span>2<span class="org-type">*</span>inv(a)<span class="org-type">*</span>psi<span class="org-type">'</span>)<span class="org-type">*</span>M;
|
||||
K = <span class="org-type">-</span>0.5<span class="org-type">*</span>inv(real(psi<span class="org-type">*</span>inv(lambda)<span class="org-type">*</span>inv(a)<span class="org-type">*</span>psi<span class="org-type">'</span>));
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
From <a class='org-ref-reference' href="#ewins00_modal">ewins00_modal</a>
|
||||
From (<a href="#citeproc_bib_item_1">Ewins 2000</a>)
|
||||
</p>
|
||||
|
||||
\begin{align}
|
||||
@@ -378,8 +128,8 @@ From <a class='org-ref-reference' href="#ewins00_modal">ewins00_modal</a>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgdaaea25" class="outline-2">
|
||||
<h2 id="orgdaaea25"><span class="section-number-2">3</span> Some notes about constraining the number of degrees of freedom</h2>
|
||||
<div id="outline-container-orgcc897f4" class="outline-2">
|
||||
<h2 id="orgcc897f4"><span class="section-number-2">3</span> Some notes about constraining the number of degrees of freedom</h2>
|
||||
<div class="outline-text-2" id="text-3">
|
||||
<p>
|
||||
We want to have the two eigen matrices.
|
||||
@@ -492,16 +242,17 @@ Is it meaningful to compare mode shapes as they give no information about the am
|
||||
</div>
|
||||
<p>
|
||||
|
||||
<h1 class='org-ref-bib-h1'>Bibliography</h1>
|
||||
<ul class='org-ref-bib'><li><a id="wang11_extrac_real_modes_physic_matric">[wang11_extrac_real_modes_physic_matric]</a> <a name="wang11_extrac_real_modes_physic_matric"></a>Tong Wang, Lingmi Zhang & Kong Fah Tee, Extraction of Real Modes and Physical Matrices From Modal Testing, <i>Earthquake Engineering and Engineering Vibration</i>, <b>10(2)</b>, 219-227 (2011). <a href="https://doi.org/10.1007/s11803-011-0060-6">link</a>. <a href="http://dx.doi.org/10.1007/s11803-011-0060-6">doi</a>.</li>
|
||||
<li><a id="ewins00_modal">[ewins00_modal]</a> <a name="ewins00_modal"></a>Ewins, Modal testing: theory, practice and application, Wiley-Blackwell (2000).</li>
|
||||
</ul>
|
||||
</p>
|
||||
|
||||
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><h2 class='citeproc-org-bib-h2'>Bibliography</h2>
|
||||
<div class="csl-bib-body">
|
||||
<div class="csl-entry"><a name="citeproc_bib_item_1"></a>Ewins, DJ. 2000. <i>Modal Testing: Theory, Practice and Application</i>. <i>Research Studies Pre, 2nd Ed., ISBN-13</i>. Baldock, Hertfordshire, England Philadelphia, PA: Wiley-Blackwell.</div>
|
||||
<div class="csl-entry"><a name="citeproc_bib_item_2"></a>Wang, Tong, Lingmi Zhang, and Kong Fah Tee. 2011. “Extraction of Real Modes and Physical Matrices from Modal Testing.” <i>Earthquake Engineering and Engineering Vibration</i> 10 (2):219–27. <a href="https://doi.org/10.1007/s11803-011-0060-6">https://doi.org/10.1007/s11803-011-0060-6</a>.</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2019-10-08 mar. 10:48</p>
|
||||
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||
<p class="date">Created: 2020-11-12 jeu. 10:29</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
Reference in New Issue
Block a user