80 lines
3.7 KiB
Org Mode
80 lines
3.7 KiB
Org Mode
#+TITLE: Modal Analysis of the ID31 Micro-Station
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:DRAWER:
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#+STARTUP: overview
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#+LANGUAGE: en
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#+EMAIL: dehaeze.thomas@gmail.com
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#+AUTHOR: Dehaeze Thomas
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#+HTML_LINK_HOME: ../index.html
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#+HTML_LINK_UP: ../index.html
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#+HTML_MATHJAX: align: center tagside: right font: TeX
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:END:
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The goal is to experimentally extract a *Spatial Model* (mass, damping, stiffness) of the structure (shown on figure [[fig:nass_picture]]) in order to tune the Multi-Body model.
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#+name: fig:nass_picture
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#+caption: Picture of the ID31 Micro-Station. (1) Granite (2) Translation Stage (3) Tilt Stage (4) Hexapod (5) Dummy Mass
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#+attr_html: :width 500px
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[[file:img/nass_picture.png]]
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The procedure is represented on figure [[fig:vibration_analysis_procedure]] where we go from left to right.
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#+name: fig:vibration_analysis_procedure
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#+caption: Vibration Analysis Procedure
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#+attr_html: :width 400px
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[[file:img/vibration_analysis_procedure.png]]
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The steps are:
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- we obtain a *Response Model* (Frequency Response Functions) from measurements (described [[file:measurement.org][here]])
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- the response model is further converted into a *Modal Model* (Natural Frequencies and Mode Shapes) (described [[file:modal_extraction.org][here]])
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- this is converted into a *Spatial Model* with the Mass/Damping/Stiffness matrices (described [[file:mathematical_model.org][here]])
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Theses matrices will be used to tune the Simscape (multi-body) model.
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The modes we want to identify are those in the frequency range between 0Hz and 150Hz.
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#+name: tab:terminology_numbers
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#+caption: Terminology for further analysis
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| <c> | <l> | <c> |
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| Symbol | Meaning | Value |
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|--------+---------------------------------+-------|
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| $p$ | Number of solid body considered | 6 |
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| $m$ | Number of accelerometers | 23 |
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| $n$ | Number of identified modes | 21 |
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| $q$ | Number of frequency points | 801 |
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| $s$ | Number of excitation | 3 |
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#+name: tab:terminology_elements
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#+caption: Terminology for further analysis
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| <c> | <l> |
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| Symbol | Meaning |
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|-----------------+--------------------------------------|
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| $[\Lambda]$ | Complex eigen value matrix |
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| $[\Psi]$ | Complex eigen vector matrix |
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| $\omega_r$ | Eigen frequency of mode $r$ [rad/s] |
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| $\xi_r$ | Modal damping for mode $r$ |
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| $\{\psi\}_r$ | Complex mode shape of mode $r$ |
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| $[M], [C], [K]$ | Mass, damping and stiffness matrices |
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| $a_r$ | "Modal A" for mode $r$ |
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The modal analysis of the ID31 Micro-station thus consists of several parts:
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- [[file:measurement.org][Frequency Response Measurements]]
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- [[file:frf_processing.org][Frequency Response Analysis and Processing]]
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- [[file:modal_extraction.org][Modal Parameter Extraction]]
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- [[file:mathematical_model.org][Derivation of Mathematical Model]]
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#+name: fig:modal_test_procedure_vertical
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#+caption: Modal Anslysis Procedure
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#+attr_html: :width 600px
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[[file:figs/modal_test_procedure_vertical.png]]
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