## 3 Vibration Measurement and Analysis
### Experimental Modal Analysis (EMA)  
EMA is a method for applying a corrected input (force, N) to a system and receiving and analyzing the response. The system is excited by hitting it using an impact hammer that can convert the unit force according to the impact. This method is easy to perform without installing additional devices, such as exciters in the system itself, and has the advantage of changing the excitation point for impact. The sunroof system in this study is in the form of a thin, flat glass plate, considering the risk of damage from strong vibration and impact and the possibility of errors due to changes in the mass of the sunroof system. Therefore, the response according to the unit force was analyzed by exciting the system using an impact hammer instead of using an electric shaker. A vehicle sunroof is fixed to the vehicle roof system and opens by moving forward and backward depending on the before and after operation. The dynamic rigidity of the sunroof varies according to the degree of sunroof opening. Hence, it can be closed or mid-open. An actual vehicle test was conducted according to three states: closed state, mid-open state, and fully open state. The summed FRF was calculated by integrating the sensors at the attachment location to confirm the characteristics of the entire sunroof glass rather than the local FRF characteristics at the sensor attachment location. The dynamic characteristics of the entire sunroof glass were analyzed. The measurement conditions for analyzing the dynamic and vibration characteristics of the sunroof glass are as follows: bandwidth = 4096 Hz, resolution = 1 Hz, acquisition time = 1 s, amplitude scaling = RMS. An automotive sunroof system EMA test was performed. Figure 7 shows the Sum FRF analysis results in the closed state. The natural frequencies, such as 34.8 Hz, 53.1 Hz, and 85.9 Hz, were confirmed below 100 Hz, but it was difficult to judge them as the natural frequencies of the vehicle sunroof glass because the changes in amplitude and phase were small and the damping was large. Furthermore, because the dynamic stiffness was 100 kgf/mm, it was difficult to judge it as the dynamic stiffness of the glass. For the mid-open state, the Sum FRF analysis results revealed values of 26.5 Hz, 3  
In the case of the fully open state, as a result of Sum FRF analysis, natural frequencies such as 15.7 Hz, 22.2 Hz, and 28.5 Hz could be analyzed. The change in amplitude and phase was large, and the damping was small compared to the closed and mid-open states. The clearest natural frequency was confirmed, and the dynamic stiffness was also approximately 5 kgf/mm, which was closest to the physical properties of glass, as shown in Figure 9.  
Table 3 presents the natural frequency measurement results according to the sunroof state. The mode order and natural frequency of the sunroof glass showed discernible disparities when the calculated natural frequency derived in the preceding chapter was juxtaposed with the outcome of the EMA test within the frequency range of interest below 50 Hz. On the other hand, the natural frequency computed via plate theory was derived from a flat rectangular plate instead of curved sunroof glass for the sake of calculation simplicity. Figure 8: Response geometry for the modal test with a half-open sunroof: (**a**) Sum FRF in the half-open state, (**b**) sum FRF with 10 and 20 kgf/mm dynamic stiffness plots. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**State**} & \multicolumn{6}{c}{**Natural Frequency [Hz]**} \\ \cline{2-7}  & **\#1** & **\#2** & **\#3** & **\#4** & **\#5** & **\#6** \\ \hline Close & 34.785 & 53.100 & 85.949 & - & - & - \\ Mid-open & 26.490 & 33.830 & 52.011 & 93.802 & - & - \\ Full-open & 15.742 & 22.245 & 28.501 & 33.789 & 56.986 & 95.897 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Natural frequency according to the sunroof state. Figure 7: Response geometry for the modal test with a closed sunroof: (**a**) Sum FRF in the closed state, (**b**) Sum FRF with 100 kgf/mm dynamic stiffness plot.