2019-05-14 14:11:31 +02:00
<?xml version="1.0" encoding="utf-8"?>
< !DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
< html xmlns = "http://www.w3.org/1999/xhtml" lang = "en" xml:lang = "en" >
< head >
2020-11-12 10:30:56 +01:00
<!-- 2020 - 11 - 12 jeu. 10:28 -->
2019-05-14 14:11:31 +02:00
< meta http-equiv = "Content-Type" content = "text/html;charset=utf-8" / >
< title > Vibrations induced by the Slip-Ring and the Spindle< / title >
< meta name = "generator" content = "Org mode" / >
< meta name = "author" content = "Dehaeze Thomas" / >
2020-11-12 10:30:56 +01:00
< link rel = "stylesheet" type = "text/css" href = "https://research.tdehaeze.xyz/css/style.css" / >
< script type = "text/javascript" src = "https://research.tdehaeze.xyz/js/script.js" > < / script >
2019-05-14 14:11:31 +02:00
< / head >
< body >
< div id = "org-div-home-and-up" >
< a accesskey = "h" href = "../index.html" > UP < / a >
|
< a accesskey = "H" href = "../index.html" > HOME < / a >
< / div > < div id = "content" >
< 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 >
2020-11-12 10:30:56 +01:00
< li > < a href = "#org4cf6966" > 1. Experimental Setup< / a > < / li >
< li > < a href = "#org9e2bd9f" > 2. Data Analysis< / a >
2019-05-14 14:11:31 +02:00
< ul >
2020-11-12 10:30:56 +01:00
< 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 >
2019-05-14 14:11:31 +02:00
< / ul >
< / li >
< / ul >
< / div >
< / div >
2020-11-12 10:30:56 +01:00
< div id = "outline-container-org4cf6966" class = "outline-2" >
< h2 id = "org4cf6966" > < span class = "section-number-2" > 1< / span > Experimental Setup< / h2 >
2019-05-14 14:11:31 +02:00
< div class = "outline-text-2" id = "text-1" >
< p >
< b > Setup< / b > :
2020-11-12 10:30:56 +01:00
One geophone is located on the marble, the other one on the floor (see figure < a href = "#org509b52d" > 1< / a > ).
2019-05-14 14:11:31 +02:00
< / 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 >
2020-11-12 10:30:56 +01:00
< div id = "org509b52d" class = "figure" >
2019-05-14 14:11:31 +02:00
< 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 >
2020-11-12 10:30:56 +01:00
< div id = "orgcc7cff8" class = "figure" >
2019-05-14 14:11:31 +02:00
< 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 >
2020-11-12 10:30:56 +01:00
< div id = "outline-container-org9e2bd9f" class = "outline-2" >
< h2 id = "org9e2bd9f" > < span class = "section-number-2" > 2< / span > Data Analysis< / h2 >
2019-05-14 14:11:31 +02:00
< div class = "outline-text-2" id = "text-2" >
< p >
2020-11-12 10:30:56 +01:00
< a id = "org216b8bb" > < / a >
2019-05-14 14:11:31 +02:00
< / p >
2020-11-12 10:30:56 +01:00
< div class = "note" id = "org5f7cf2d" >
2019-05-14 14:11:31 +02:00
< p >
All the files (data and Matlab scripts) are accessible < a href = "data/marble_dynamics.zip" > here< / a > .
< / p >
< / div >
< / div >
2020-11-12 10:30:56 +01:00
< div id = "outline-container-org3b8531a" class = "outline-3" >
< h3 id = "org3b8531a" > < span class = "section-number-3" > 2.1< / span > Load data< / h3 >
2019-05-14 14:11:31 +02:00
< div class = "outline-text-3" id = "text-2-1" >
< div class = "org-src-container" >
2020-11-12 10:30:56 +01:00
< 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;
2019-05-14 14:11:31 +02:00
< / pre >
< / div >
< / div >
< / div >
2020-11-12 10:30:56 +01:00
< div id = "outline-container-orgf20b247" class = "outline-3" >
< h3 id = "orgf20b247" > < span class = "section-number-3" > 2.2< / span > Time domain plots< / h3 >
2019-05-14 14:11:31 +02:00
< 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 > ;
2020-11-12 10:30:56 +01:00
subplot(1, 3, 1);
2019-05-14 14:11:31 +02:00
hold on;
2020-11-12 10:30:56 +01:00
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 > );
2019-05-14 14:11:31 +02:00
hold off;
2020-11-12 10:30:56 +01:00
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 > );
2019-05-14 14:11:31 +02:00
2020-11-12 10:30:56 +01:00
subplot(1, 3, 2);
2019-05-14 14:11:31 +02:00
hold on;
2020-11-12 10:30:56 +01:00
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 > );
2019-05-14 14:11:31 +02:00
hold off;
2020-11-12 10:30:56 +01:00
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 > );
2019-05-14 14:11:31 +02:00
2020-11-12 10:30:56 +01:00
subplot(1, 3, 3);
2019-05-14 14:11:31 +02:00
hold on;
2020-11-12 10:30:56 +01:00
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 > );
2019-05-14 14:11:31 +02:00
hold off;
2020-11-12 10:30:56 +01:00
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 > );
2019-05-14 14:11:31 +02:00
< / pre >
< / div >
2020-11-12 10:30:56 +01:00
< div id = "org79e8540" class = "figure" >
2019-05-14 14:11:31 +02:00
< 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 >
2020-11-12 10:30:56 +01:00
< 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 >
2019-05-14 14:11:31 +02:00
< 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" >
2020-11-12 10:30:56 +01:00
< pre class = "src src-matlab" > dt = m_z(2, 3)< span class = "org-type" > -< / span > m_z(1, 3);
2019-05-14 14:11:31 +02:00
2020-11-12 10:30:56 +01:00
Fs = 1< span class = "org-type" > /< / span > dt; < span class = "org-comment" > % [Hz]< / span >
2019-05-14 14:11:31 +02:00
2020-11-12 10:30:56 +01:00
win = hanning(ceil(10< span class = "org-type" > *< / span > Fs));
2019-05-14 14:11:31 +02:00
< / pre >
< / div >
< p >
Then we compute the Power Spectral Density using < code > pwelch< / code > function.
< / p >
< div class = "org-src-container" >
2020-11-12 10:30:56 +01:00
< 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);
2019-05-14 14:11:31 +02:00
2020-11-12 10:30:56 +01:00
[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);
2019-05-14 14:11:31 +02:00
2020-11-12 10:30:56 +01:00
[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);
2019-05-14 14:11:31 +02:00
< / pre >
< / div >
< p >
2020-11-12 10:30:56 +01:00
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.
2019-05-14 14:11:31 +02:00
< / p >
2020-11-12 10:30:56 +01:00
< div id = "orga9e6519" class = "figure" >
2019-05-14 14:11:31 +02:00
< 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 >
2020-11-12 10:30:56 +01:00
< div id = "orgdb1e6aa" class = "figure" >
2019-05-14 14:11:31 +02:00
< 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 >
2020-11-12 10:30:56 +01:00
< div id = "orgc40ceda" class = "figure" >
2019-05-14 14:11:31 +02:00
< 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 >
2020-11-12 10:30:56 +01:00
< 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 >
2019-05-14 14:11:31 +02:00
< 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 >
2020-11-12 10:30:56 +01:00
The result is shown on figure < a href = "#orgc536396" > 7< / a > .
2019-05-14 14:11:31 +02:00
< / p >
< div class = "org-src-container" >
2020-11-12 10:30:56 +01:00
< 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);
2019-05-14 14:11:31 +02:00
< / pre >
< / div >
2020-11-12 10:30:56 +01:00
< div id = "orgc536396" class = "figure" >
2019-05-14 14:11:31 +02:00
< 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 >
2020-11-12 10:30:56 +01:00
< div id = "outline-container-org184f531" class = "outline-3" >
< h3 id = "org184f531" > < span class = "section-number-3" > 2.5< / span > Conclusion< / h3 >
2019-05-14 14:11:31 +02:00
< div class = "outline-text-3" id = "text-2-5" >
2020-11-12 10:30:56 +01:00
< div class = "important" id = "org1429884" >
2019-05-14 14:11:31 +02:00
< 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 >
2020-11-12 10:30:56 +01:00
< p class = "date" > Created: 2020-11-12 jeu. 10:28< / p >
2019-05-14 14:11:31 +02:00
< / div >
< / body >
< / html >
