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Modal Analysis of the ID31 Micro-Station

The goal is to experimentally extract a Spatial Model (mass, damping, stiffness) of the structure (shown on figure 1) in order to tune the Multi-Body model.

nass_picture.png

Figure 1: Picture of the ID31 Micro-Station. (1) Granite (2) Translation Stage (3) Tilt Stage (4) Hexapod (5) Dummy Mass

The procedure is represented on figure 2 where we go from left to right.

vibration_analysis_procedure.png

Figure 2: Vibration Analysis Procedure

The steps are:

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.

Table 1: Terminology for further analysis
Symbol Meaning Value
\(p\) Number of solid body considered 6
\(m\) Number of accelerometers 23
\(n\) Number of identified modes 21
\(q\) Number of frequency points 801
\(s\) Number of excitation 3
Table 2: Terminology for further analysis
Symbol Meaning
\([\Lambda]\) Complex eigen value matrix
\([\Psi]\) Complex eigen vector matrix
\(\omega_r\) Eigen frequency of mode \(r\) [rad/s]
\(\xi_r\) Modal damping for mode \(r\)
\(\{\psi\}_r\) Complex mode shape of mode \(r\)
\([M], [C], [K]\) Mass, damping and stiffness matrices
\(a_r\) “Modal A” for mode \(r\)

The modal analysis of the ID31 Micro-station thus consists of several parts:

modal_test_procedure_vertical.png

Figure 3: Modal Anslysis Procedure

Author: Dehaeze Thomas

Created: 2020-11-12 jeu. 10:29