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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 >
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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 = "#org9f88298" > 1< / a > ) in order to tune the Multi-Body model.
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< / p >
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< div id = "org9f88298" class = "figure" >
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< p > < img src = "img/nass_picture.png" alt = "nass_picture.png" width = "500px" / >
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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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< p >
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The procedure is represented on figure < a href = "#org9011d1b" > 2< / a > where we go from left to right.
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< / p >
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< div id = "org9011d1b" 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 > < span class = "figure-number" > Figure 2: < / span > Vibration Analysis Procedure< / p >
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< 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 >
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< p >
Theses matrices will be used to tune the Simscape (multi-body) model.
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< p >
The modes we want to identify are those in the frequency range between 0Hz and 150Hz.
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< table id = "org4211aff" 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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< col class = "org-left" / >
< col class = "org-center" / >
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< 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 >
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< td class = "org-center" > \(p\)< / td >
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< td class = "org-left" > Number of solid body considered< / td >
< td class = "org-center" > 6< / td >
< / tr >
< tr >
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< td class = "org-center" > \(m\)< / td >
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< td class = "org-left" > Number of accelerometers< / td >
< td class = "org-center" > 23< / td >
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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 >
< td class = "org-center" > 21< / td >
< / tr >
< tr >
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< td class = "org-center" > \(q\)< / td >
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< td class = "org-left" > Number of frequency points< / td >
< td class = "org-center" > 801< / td >
< / tr >
< tr >
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< td class = "org-center" > \(s\)< / td >
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< td class = "org-left" > Number of excitation< / td >
< td class = "org-center" > 3< / td >
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< / tbody >
< / table >
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< table id = "orgc9968b6" 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 >
< 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 >
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< td class = "org-center" > \([\Lambda]\)< / td >
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< 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 >
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< td class = "org-left" > “ Modal A” for mode \(r\)< / td >
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< / tr >
< / tbody >
< / table >
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< p >
The modal analysis of the ID31 Micro-station thus consists of several parts:
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< / p >
< 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 >
< li > < a href = "mathematical_model.html" > Derivation of Mathematical Model< / a > < / li >
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< / ul >
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< div id = "org3b7e193" class = "figure" >
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< p > < img src = "figs/modal_test_procedure_vertical.png" alt = "modal_test_procedure_vertical.png" width = "600px" / >
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< p > < span class = "figure-number" > Figure 3: < / span > Modal Anslysis Procedure< / p >
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< div id = "postamble" class = "status" >
< p class = "author" > Author: Dehaeze Thomas< / p >
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< p class = "date" > Created: 2020-11-12 jeu. 10:29< / p >
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