## 3 Vibration Measurement and Analysis
### Experimental Setting  
Conducting an experimental modal analysis according to the driving vibration of a vehicle sunroof requires setting the response position according to the driving vibration. The response position should be selected so the analysis results based on vibration can clearly identify the mode shape of the frequency band of interest. In the case of a vehicle sunroof, the response position should be selected as a grid in the form of a wide plate,  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \(i\) & \(m\) & \(n\) & \(16\left(\frac{\pi}{\pi}\right)^{2}\left(\frac{\phi k}{D}\right)^{12}\Omega_{i}\) \\ \hline
1 & 1 & 1 & 25 \\
2 & 1 & 2 & 52 \\
3 & 2 & 1 & 73 \\
4 & 1 & 3 & 97 \\
5 & 2 & 2 & 100 \\
6 & 2 & 3 & 145 \\
7 & 3 & 1 & 153 \\
8 & 1 & 4 & 160 \\
9 & 3 & 2 & 180 \\
10 & 2 & 4 & 208 \\
11 & 3 & 3 & 225 \\
12 & 4 & 1 & 265 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Natural frequencies of a rectangular plate (a/b = 4:3).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \(i\) & \(m\) & \(n\) & \(16\left(\frac{\pi}{\pi}\right)^{2}\left(\frac{\phi k}{D}\right)^{12}\Omega_{i}\) \\ \hline
1 & 1 & 1 & 25 \\
2 & 1 & 2 & 52 \\
3 & 2 & 1 & 73 \\
4 & 1 & 3 & 97 \\
5 & 2 & 2 & 100 \\
7 & 3 & 1 & 153 \\
9 & 3 & 2 & 180 \\
11 & 3 & 3 & 225 \\
12 & 4 & 1 & 265 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Natural frequencies of a rectangular plate (a/b = 4:3).  
and an accelerometer should be attached (Figure 4). In addition, the wavelength of the structure decreases as the frequency of interest increases, and higher-order mode shapes occur. Hence, the distance between the individual response positions must be reduced. Nevertheless, in the case of vehicle sunroof vibration, the main resonance occurs in the low-frequency band of 100 Hz or less. Given this background, the sensor was attached with the distance between accelerations set to approximately 500 mm.  
The response geometry was defined using software that analyzes the vibration response data of the structure through the exciting forces generated from vehicle systems, such as the engine and tires, when the vehicle is driven and confirms the structural mode in the experimental main frequency band, as shown in Figure 5.  
The response geometry was defined by dividing it into the frame assembly, rail part, and vehicle sunroof glass part, up to the sunroof glass, which is the final structure through which exciting force is transmitted. The response geometry was defined as blue for the glass part of the vehicle sunroof, pink for the mechanism rail part, and orange for the frame assembly part. One of the critical parts when defining the response geometry is that all modes in the frequency band of interest must be excited, and the geometry position must be anticipated and set according to the system structure to avoid interference caused by resonance unrelated to the target mode.  
Car sunroof glass has a wide rectangular plate structure, and the geometry of the middle part (G:2, G:4, G:6, G:7, G:8, G:9, G:10, G:12, G:14, G:16, G:17, G:18, G:19, G:20, G:22, G:24) is set. In addition, the rail and frame assembly parts were designed to predict the bending mode shape by setting the connection part geometry (R:2, R:4, R:7, R:9, B:2, B:4, B:7, B: 9, B:11, B:13). The equipment for the test measurement was a SIEMENS LMS SCADAS Recorder (SCR209), and the software for analysis was S  
Figure 4: Location of the accelerometers on a vehicle sunroof.  
Figure 5: Response geometry for the modal test of a sunroof system.  
Triaxial accelerometers (PCB 356A15) with a sensitivity of 100 mV/g (1.2 mV/(m/s\({}^{2}\))) and a measurement range of \(\pm\)50 g pk (\(\pm\)490 pk) were attached to the sunroof system for acceleration measurements, and an impulse force hammer (PCB 086D20) with a sensitivity of 0.244 mV/N was utilized for system excitation. Figure 6 shows the schematic diagram for the modal test setup.