nass-micro-station-measurements/modal-analysis/mathematical_model.org

#+TITLE: Modal Analysis - Derivation of Mathematical Models
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#+STARTUP: overview

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

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* Type of Model
The model that we want to obtain is a *multi-body model*.
It is composed of several *solid bodies connected with springs and dampers*.
The solid bodies are represented with different colors on figure [[fig:nass_solidworks]].

In the simscape model, the solid bodies are:
- the granite (1 or 2 solids)
- the translation stage
- the tilt stage
- the spindle and slip-ring
- the hexapod

#+name: fig:nass_solidworks
#+caption: CAD view of the ID31 Micro-Station
#+attr_html: :width 800px
[[file:img/nass_solidworks.png]]

However, each of the DOF of the system may not be relevant for the modes present in the frequency band of interest.
For instance, the translation stage may not vibrate in the Z direction for all the modes identified. Then, we can block this DOF and this simplifies the model.

The modal identification done here will thus permit us to determine *which DOF can be neglected*.