438 lines
15 KiB
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438 lines
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HTML
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<title>Modal Analysis of the ID31 Micro-Station</title>
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<div id="org-div-home-and-up">
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<a accesskey="h" href="../index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Modal Analysis of the ID31 Micro-Station</h1>
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<p>
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The goal is to experimentally extract a <b>Spatial Model</b> (mass, damping, stiffness) of the structure (shown on figure <a href="#org4a31989">1</a>) in order to tune the Multi-Body model.
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</p>
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<div id="org4a31989" class="figure">
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<p><img src="img/nass_picture.png" alt="nass_picture.png" width="500px" />
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</p>
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<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>
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</div>
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<p>
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The procedure is represented on figure <a href="#org4a4053c">2</a> where we go from left to right.
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</p>
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<div id="org4a4053c" class="figure">
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<p><img src="img/vibration_analysis_procedure.png" alt="vibration_analysis_procedure.png" width="400px" />
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</p>
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<p><span class="figure-number">Figure 2: </span>Vibration Analysis Procedure</p>
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</div>
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<p>
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The steps are:
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</p>
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<ul class="org-ul">
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<li>we obtain a <b>Response Model</b> (Frequency Response Functions) from measurements (described <a href="measurement.html">here</a>)</li>
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<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>
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<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>
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</ul>
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<p>
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Theses matrices will be used to tune the Simscape (multi-body) model.
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</p>
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<p>
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The modes we want to identify are those in the frequency range between 0Hz and 150Hz.
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</p>
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<table id="org890b40f" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<caption class="t-above"><span class="table-number">Table 1:</span> Terminology for further analysis</caption>
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<th scope="col" class="org-center">Symbol</th>
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<th scope="col" class="org-left">Meaning</th>
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<th scope="col" class="org-center">Value</th>
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<td class="org-center">\(S\)</td>
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<td class="org-left">Number of solid body considered</td>
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<td class="org-center">6</td>
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</tr>
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<tr>
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<td class="org-center">\(M\)</td>
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<td class="org-left">Number of accelerometers</td>
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<td class="org-center">23</td>
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</tr>
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<tr>
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<td class="org-center">\(N\)</td>
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<td class="org-left">Number of identified modes</td>
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<td class="org-center">21</td>
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</tr>
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<tr>
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<td class="org-center">\(p\)</td>
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<td class="org-left">Number of frequency points</td>
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<td class="org-center">801</td>
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</tr>
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<tr>
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<td class="org-center">\(E\)</td>
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<td class="org-left">Number of excitation</td>
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<td class="org-center">3</td>
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</tr>
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</tbody>
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</table>
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<table id="orgbda6b99" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<caption class="t-above"><span class="table-number">Table 2:</span> Terminology for further analysis</caption>
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<colgroup>
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<col class="org-center" />
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<col class="org-left" />
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</colgroup>
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<thead>
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<tr>
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<th scope="col" class="org-center">Symbol</th>
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<th scope="col" class="org-left">Meaning</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td class="org-center">\(\Lambda\)</td>
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<td class="org-left">Complex eigen value matrix</td>
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</tr>
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<tr>
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<td class="org-center">\([\Psi]\)</td>
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<td class="org-left">Complex eigen vector matrix</td>
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</tr>
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<tr>
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<td class="org-center">\(\omega_r\)</td>
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<td class="org-left">Eigen frequency of mode \(r\) [rad/s]</td>
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</tr>
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<tr>
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<td class="org-center">\(\xi_r\)</td>
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<td class="org-left">Modal damping for mode \(r\)</td>
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</tr>
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<tr>
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<td class="org-center">\(\{\psi\}_r\)</td>
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<td class="org-left">Complex mode shape of mode \(r\)</td>
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</tr>
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<tr>
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<td class="org-center">\([M], [C], [K]\)</td>
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<td class="org-left">Mass, damping and stiffness matrices</td>
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</tr>
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<tr>
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<td class="org-center">\(a_r\)</td>
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<td class="org-left">"Modal A" for mode \(r\)</td>
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</tr>
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</tbody>
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</table>
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<p>
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The modal analysis of the ID31 Micro-station thus consists of several parts:
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</p>
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<ul class="org-ul">
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<li><a href="measurement.html">Frequency Response Measurements</a></li>
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<li><a href="frf_processing.html">Frequency Response Analysis and Processing</a></li>
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<li><a href="modal_extraction.html">Modal Parameter Extraction</a></li>
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<li><a href="mathematical_model.html">Derivation of Mathematical Model</a></li>
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</ul>
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</div>
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<div id="postamble" class="status">
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<p class="author">Author: Dehaeze Thomas</p>
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<p class="date">Created: 2019-07-12 ven. 11:24</p>
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<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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</div>
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</body>
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</html>
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