#+TITLE: Modal Analysis of the ID31 Micro-Station
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#+STARTUP: overview

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#+EMAIL: dehaeze.thomas@gmail.com
#+AUTHOR: Dehaeze Thomas

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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.

#+name: fig:nass_picture
#+caption: Picture of the ID31 Micro-Station. (1) Granite (2) Translation Stage (3) Tilt Stage (4) Hexapod (5) Dummy Mass
#+attr_html: :width 500px
[[file:img/nass_picture.png]]

The procedure is represented on figure [[fig:vibration_analysis_procedure]] where we go from left to right.

#+name: fig:vibration_analysis_procedure
#+caption: Vibration Analysis Procedure
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[[file:img/vibration_analysis_procedure.png]]

The steps are:
- we obtain a *Response Model* (Frequency Response Functions) from measurements (described [[file:measurement.org][here]])
- the response model is further converted into a *Modal Model* (Natural Frequencies and Mode Shapes) (described [[file:modal_extraction.org][here]])
- this is converted into a *Spatial Model* with the Mass/Damping/Stiffness matrices (described [[file:mathematical_model.org][here]])

Theses matrices will be used to tune the Simscape (multi-body) model.

The modes we want to identify are those in the frequency range between 0Hz and 150Hz.


The modal analysis of the ID31 Micro-station thus consists of several parts:
- [[file:measurement.org][Frequency Response Measurements]]
- [[file:frf_processing.org][Frequency Response Analysis and Processing]]
- [[file:modal_extraction.org][Modal Parameter Extraction]]
- [[file:mathematical_model.org][Derivation of Mathematical Model]]