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.

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.

Figure 2: Vibration Analysis Procedure

The steps are:

we obtain a Response Model (Frequency Response Functions) from measurements (described here)
the response model is further converted into a Modal Model (Natural Frequencies and Mode Shapes) (described here)
this is converted into a Spatial Model with the Mass/Damping/Stiffness matrices (described 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.

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:

Figure 3: Modal Anslysis Procedure