nass-micro-station-measurem.../dynamical-meas-granite/index.html

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<title>Vibrations induced by the Slip-Ring and the Spindle</title>
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<h1 class="title">Vibrations induced by the Slip-Ring and the Spindle</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org4cf6966">1. Experimental Setup</a></li>
<li><a href="#org9e2bd9f">2. Data Analysis</a>
<ul>
<li><a href="#org3b8531a">2.1. Load data</a></li>
<li><a href="#orgf20b247">2.2. Time domain plots</a></li>
<li><a href="#org581339a">2.3. Compute the power spectral densities</a></li>
<li><a href="#orgdfd290d">2.4. Compute the transfer function from floor motion to ground motion</a></li>
<li><a href="#org184f531">2.5. Conclusion</a></li>
</ul>
</li>
</ul>
</div>
</div>

<div id="outline-container-org4cf6966" class="outline-2">
<h2 id="org4cf6966"><span class="section-number-2">1</span> Experimental Setup</h2>
<div class="outline-text-2" id="text-1">
<p>
<b>Setup</b>:
One geophone is located on the marble, the other one on the floor (see figure <a href="#org509b52d">1</a>).
</p>


<p>
Two geophone are use:
</p>
<ul class="org-ul">
<li>One on the floor (corresponding to the first column in the data)</li>
<li>One at the marble location (corresponding to the second column in the data)</li>
</ul>

<p>
Two voltage amplifiers are used, their setup is:
</p>
<ul class="org-ul">
<li>gain of 60dB</li>
<li>AC/DC switch on AC</li>
<li>Low pass filter at 1kHz</li>
</ul>

<p>
A first order low pass filter is also added at the input of the voltage amplifiers.
</p>

<p>
<b>Goal</b>:
</p>
<ul class="org-ul">
<li>Identify the marble dynamics in all the directions</li>
</ul>


<p>
<b>Measurements</b>:
Three measurements are done:
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">


<colgroup>
<col  class="org-left" />

<col  class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Measurement File</th>
<th scope="col" class="org-left">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left"><code>mat/data_037.mat</code></td>
<td class="org-left">Z direction</td>
</tr>

<tr>
<td class="org-left"><code>mat/data_038.mat</code></td>
<td class="org-left">N direction</td>
</tr>

<tr>
<td class="org-left"><code>mat/data_039.mat</code></td>
<td class="org-left">E direction</td>
</tr>
</tbody>
</table>

<p>
Each of the measurement <code>mat</code> file contains one <code>data</code> array with 3 columns:
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">


<colgroup>
<col  class="org-right" />

<col  class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-right">Column number</th>
<th scope="col" class="org-left">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-right">1</td>
<td class="org-left">Geophone - Floor</td>
</tr>

<tr>
<td class="org-right">2</td>
<td class="org-left">Geophone - Marble</td>
</tr>

<tr>
<td class="org-right">3</td>
<td class="org-left">Time</td>
</tr>
</tbody>
</table>


<div id="org509b52d" class="figure">
<p><img src="./img/IMG_20190513_161729.jpg" alt="IMG_20190513_161729.jpg" width="500px" />
</p>
<p><span class="figure-number">Figure 1: </span>Picture of the experimental setup</p>
</div>


<div id="orgcc7cff8" class="figure">
<p><img src="./img/IMG_20190513_161718.jpg" alt="IMG_20190513_161718.jpg" width="500px" />
</p>
<p><span class="figure-number">Figure 2: </span>Picture of the experimental setup</p>
</div>
</div>
</div>

<div id="outline-container-org9e2bd9f" class="outline-2">
<h2 id="org9e2bd9f"><span class="section-number-2">2</span> Data Analysis</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="org216b8bb"></a>
</p>
<div class="note" id="org5f7cf2d">
<p>
All the files (data and Matlab scripts) are accessible <a href="data/marble_dynamics.zip">here</a>.
</p>

</div>
</div>

<div id="outline-container-org3b8531a" class="outline-3">
<h3 id="org3b8531a"><span class="section-number-3">2.1</span> Load data</h3>
<div class="outline-text-3" id="text-2-1">
<div class="org-src-container">
<pre class="src src-matlab">m_z = load(<span class="org-string">'mat/data_037.mat'</span>, <span class="org-string">'data'</span>); m_z = m_z.data;
m_n = load(<span class="org-string">'mat/data_038.mat'</span>, <span class="org-string">'data'</span>); m_n = m_n.data;
m_e = load(<span class="org-string">'mat/data_039.mat'</span>, <span class="org-string">'data'</span>); m_e = m_e.data;
</pre>
</div>
</div>
</div>

<div id="outline-container-orgf20b247" class="outline-3">
<h3 id="orgf20b247"><span class="section-number-3">2.2</span> Time domain plots</h3>
<div class="outline-text-3" id="text-2-2">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
subplot(1, 3, 1);
hold on;
plot(m_z(<span class="org-type">:</span>, 3), m_z(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Marble - Z'</span>);
plot(m_z(<span class="org-type">:</span>, 3), m_z(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Floor - Z'</span>);
hold off;
xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Voltage [V]'</span>);
xlim([0, 100]); ylim([<span class="org-type">-</span>2 2]);
legend(<span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);

subplot(1, 3, 2);
hold on;
plot(m_n(<span class="org-type">:</span>, 3), m_n(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Marble - N'</span>);
plot(m_n(<span class="org-type">:</span>, 3), m_n(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Floor - N'</span>);
hold off;
xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Voltage [V]'</span>);
xlim([0, 100]); ylim([<span class="org-type">-</span>2 2]);
legend(<span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);

subplot(1, 3, 3);
hold on;
plot(m_e(<span class="org-type">:</span>, 3), m_e(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Marble - E'</span>);
plot(m_e(<span class="org-type">:</span>, 3), m_e(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Floor - E'</span>);
hold off;
xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Voltage [V]'</span>);
xlim([0, 100]); ylim([<span class="org-type">-</span>2 2]);
legend(<span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
</pre>
</div>


<div id="org79e8540" class="figure">
<p><img src="figs/marble_floor_motion_time.png" alt="marble_floor_motion_time.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Floor and ground motion</p>
</div>
</div>
</div>

<div id="outline-container-org581339a" class="outline-3">
<h3 id="org581339a"><span class="section-number-3">2.3</span> Compute the power spectral densities</h3>
<div class="outline-text-3" id="text-2-3">
<p>
We first compute some parameters that will be used for the PSD computation.
</p>
<div class="org-src-container">
<pre class="src src-matlab">dt = m_z(2, 3)<span class="org-type">-</span>m_z(1, 3);

Fs = 1<span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>

win = hanning(ceil(10<span class="org-type">*</span>Fs));
</pre>
</div>

<p>
Then we compute the Power Spectral Density using <code>pwelch</code> function.
</p>
<div class="org-src-container">
<pre class="src src-matlab">[px_fz, f] = pwelch(m_z(<span class="org-type">:</span>, 1), win, [], [], Fs);
[px_gz, <span class="org-type">~</span>] = pwelch(m_z(<span class="org-type">:</span>, 2), win, [], [], Fs);

[px_fn, <span class="org-type">~</span>] = pwelch(m_n(<span class="org-type">:</span>, 1), win, [], [], Fs);
[px_gn, <span class="org-type">~</span>] = pwelch(m_n(<span class="org-type">:</span>, 2), win, [], [], Fs);

[px_fe, <span class="org-type">~</span>] = pwelch(m_e(<span class="org-type">:</span>, 1), win, [], [], Fs);
[px_ge, <span class="org-type">~</span>] = pwelch(m_e(<span class="org-type">:</span>, 2), win, [], [], Fs);
</pre>
</div>


<p>
The results are shown on figure <a href="#orga9e6519">4</a> for the Z direction, figure <a href="#orgdb1e6aa">5</a> for the north direction, and figure <a href="#orgc40ceda">6</a> for the east direction.
</p>


<div id="orga9e6519" class="figure">
<p><img src="figs/floor_marble_psd_z.png" alt="floor_marble_psd_z.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Amplitude Spectral Density of the measured voltage corresponding to the geophone located on the floor and on the marble - Z direction</p>
</div>


<div id="orgdb1e6aa" class="figure">
<p><img src="figs/floor_marble_psd_n.png" alt="floor_marble_psd_n.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the measured voltage corresponding to the geophone located on the floor and on the marble - N direction</p>
</div>


<div id="orgc40ceda" class="figure">
<p><img src="figs/floor_marble_psd_e.png" alt="floor_marble_psd_e.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Amplitude Spectral Density of the measured voltage corresponding to the geophone located on the floor and on the marble - E direction</p>
</div>
</div>
</div>

<div id="outline-container-orgdfd290d" class="outline-3">
<h3 id="orgdfd290d"><span class="section-number-3">2.4</span> Compute the transfer function from floor motion to ground motion</h3>
<div class="outline-text-3" id="text-2-4">
<p>
We now compute the transfer function from the floor motion to the granite motion.
</p>

<p>
The result is shown on figure <a href="#orgc536396">7</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">[TZ, f] = tfestimate(m_z(<span class="org-type">:</span>, 1), <span class="org-type">-</span>m_z(<span class="org-type">:</span>, 2), win, [], [], Fs);
[TN, <span class="org-type">~</span>] = tfestimate(m_n(<span class="org-type">:</span>, 1), <span class="org-type">-</span>m_n(<span class="org-type">:</span>, 2), win, [], [], Fs);
[TE, <span class="org-type">~</span>] = tfestimate(m_e(<span class="org-type">:</span>, 1), <span class="org-type">-</span>m_e(<span class="org-type">:</span>, 2), win, [], [], Fs);
</pre>
</div>


<div id="orgc536396" class="figure">
<p><img src="figs/tf_granite.png" alt="tf_granite.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Transfer function from floor motion to granite motion</p>
</div>
</div>
</div>

<div id="outline-container-org184f531" class="outline-3">
<h3 id="org184f531"><span class="section-number-3">2.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-5">
<div class="important" id="org1429884">
<ul class="org-ul">
<li>We see resonance of the granite at 33Hz in the horizontal directions</li>
<li>We see two resonances for the z direction: at 60Hz and 75Hz</li>
</ul>

</div>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-11-12 jeu. 10:28</p>
</div>
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