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<title>Modal Analysis of the ID31 Micro-Station</title>
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<h1 class="title">Modal Analysis of the ID31 Micro-Station</h1>
<p>
The goal is to experimentally extract a <b>Spatial Model</b> (mass, damping, stiffness) of the structure (shown on figure <a href="#org9f88298">1</a>) in order to tune the Multi-Body model.
</p>
<div id="org9f88298" class="figure">
<p><img src="img/nass_picture.png" alt="nass_picture.png" width="500px" />
</p>
<p><span class="figure-number">Figure 1: </span>Picture of the ID31 Micro-Station. (1) Granite (2) Translation Stage (3) Tilt Stage (4) Hexapod (5) Dummy Mass</p>
</div>
<p>
The procedure is represented on figure <a href="#org9011d1b">2</a> where we go from left to right.
</p>
<div id="org9011d1b" class="figure">
<p><img src="img/vibration_analysis_procedure.png" alt="vibration_analysis_procedure.png" width="400px" />
</p>
<p><span class="figure-number">Figure 2: </span>Vibration Analysis Procedure</p>
</div>
<p>
The steps are:
</p>
<ul class="org-ul">
<li>we obtain a <b>Response Model</b> (Frequency Response Functions) from measurements (described <a href="measurement.html">here</a>)</li>
<li>the response model is further converted into a <b>Modal Model</b> (Natural Frequencies and Mode Shapes) (described <a href="modal_extraction.html">here</a>)</li>
<li>this is converted into a <b>Spatial Model</b> with the Mass/Damping/Stiffness matrices (described <a href="mathematical_model.html">here</a>)</li>
</ul>
<p>
Theses matrices will be used to tune the Simscape (multi-body) model.
</p>
<p>
The modes we want to identify are those in the frequency range between 0Hz and 150Hz.
</p>
<table id="org4211aff" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Terminology for further analysis</caption>
<colgroup>
<col class="org-center" />
<col class="org-left" />
<col class="org-center" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-center">Symbol</th>
<th scope="col" class="org-left">Meaning</th>
<th scope="col" class="org-center">Value</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-center">\(p\)</td>
<td class="org-left">Number of solid body considered</td>
<td class="org-center">6</td>
</tr>
<tr>
<td class="org-center">\(m\)</td>
<td class="org-left">Number of accelerometers</td>
<td class="org-center">23</td>
</tr>
<tr>
<td class="org-center">\(n\)</td>
<td class="org-left">Number of identified modes</td>
<td class="org-center">21</td>
</tr>
<tr>
<td class="org-center">\(q\)</td>
<td class="org-left">Number of frequency points</td>
<td class="org-center">801</td>
</tr>
<tr>
<td class="org-center">\(s\)</td>
<td class="org-left">Number of excitation</td>
<td class="org-center">3</td>
</tr>
</tbody>
</table>
<table id="orgc9968b6" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 2:</span> Terminology for further analysis</caption>
<colgroup>
<col class="org-center" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-center">Symbol</th>
<th scope="col" class="org-left">Meaning</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-center">\([\Lambda]\)</td>
<td class="org-left">Complex eigen value matrix</td>
</tr>
<tr>
<td class="org-center">\([\Psi]\)</td>
<td class="org-left">Complex eigen vector matrix</td>
</tr>
<tr>
<td class="org-center">\(\omega_r\)</td>
<td class="org-left">Eigen frequency of mode \(r\) [rad/s]</td>
</tr>
<tr>
<td class="org-center">\(\xi_r\)</td>
<td class="org-left">Modal damping for mode \(r\)</td>
</tr>
<tr>
<td class="org-center">\(\{\psi\}_r\)</td>
<td class="org-left">Complex mode shape of mode \(r\)</td>
</tr>
<tr>
<td class="org-center">\([M], [C], [K]\)</td>
<td class="org-left">Mass, damping and stiffness matrices</td>
</tr>
<tr>
<td class="org-center">\(a_r\)</td>
<td class="org-left">&ldquo;Modal A&rdquo; for mode \(r\)</td>
</tr>
</tbody>
</table>
<p>
The modal analysis of the ID31 Micro-station thus consists of several parts:
</p>
<ul class="org-ul">
<li><a href="measurement.html">Frequency Response Measurements</a></li>
<li><a href="frf_processing.html">Frequency Response Analysis and Processing</a></li>
<li><a href="modal_extraction.html">Modal Parameter Extraction</a></li>
<li><a href="mathematical_model.html">Derivation of Mathematical Model</a></li>
</ul>
<div id="org3b7e193" class="figure">
<p><img src="figs/modal_test_procedure_vertical.png" alt="modal_test_procedure_vertical.png" width="600px" />
</p>
<p><span class="figure-number">Figure 3: </span>Modal Anslysis Procedure</p>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-11-12 jeu. 10:29</p>
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