# Mechanical Structure Design and Experimental Study of Gamma-ray Monitor for Small Satellite Payload
## 4 Simulation and Experimental Results
### Dynamical Analysis
#### 4.2.3 Random Vibration Analysis
High frequency characteristics are more sensitive to structural details, and the finite element mesh needs to be gradually encrypted with the increase in frequency band width, but the calculation scale will expand rapidly, so the high frequency numerical results have large errors [36]. In the finite element analysis of this paper, according to experience, the initial value of damping is taken as 0.03, and there is a large error between the total root mean square of the acceleration analysis results and the experimental results, as shown in Table 8. Therefore, the parameter method is adopted for the finite element model correction. According to the sweep frequency test results of sinusoidal characteristic in Figure 10 and the half-power bandwidth method [37], the damping value in X direction is 0.013, while the values are 0.029 in Y direction and 0.02 in Z direction, respectively. The damping value obtained by the 0.5 g sweep frequency is used as the input parameter of structural damping, and the random vibration analysis is carried out after the finite element model is modified. The corrected values are compared with the experimental values, as shown in Table 9. It can be seen from Table 9 that the overall errors between the model correction results and the experimental results are reduced, which indicates the effectiveness of the finite element model correction and provides guidance for the subsequent optimization design. After the identification level random vibration test, a 0.5 g sinusoidal characteristic sweep frequency test was conducted to verify the integrity of the structure. The results are shown in Figure 13.  
From the sinusoidal characteristic sweep frequency curves before and after the random vibration test of measuring points in X, Y and Z directions in Figure 13, it can be concluded that the sweep frequency curves of each measuring point before and after the random vibration test coincide well. The frequency drift of the first order dominant frequency is less than 1.0% before and after the random vibration experiment at the X identification level, while the same drift in Y direction is less than 2.0% and the drift in Z direction is less than 5.0%. The structure is therefore safe and meets the requirements under random excitation. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{**Measurement Points**} & \multirow{2}{*}{**Categories**} & \multicolumn{2}{c}{**X-Direction**} & \multicolumn{2}{c}{**Y-Direction**} & \multicolumn{2}{c}{**Z-Direction**} \\ \cline{3-8}  & & **Grms (g\({}^{2}\)/Hz)** & & **Magnification** & **Grms (g\({}^{2}\)/Hz)** & & **Magnification** & **Grms (g\({}^{2}\)/Hz)** & **Magnification** \\ \hline \multirow{3}{*}{1} & Analysis & 37.50 & 3.55 & 29.07 & 2.75 & 32.66 & 3.09 \\  & Test & 56.16 & 5.31 & 29.31 & 2.77 & 54.29 & 5.13 \\  & Error & & \(-\)33\% & & \(-\)0.8\% & & \(-\)39.8\% \\ \hline \multirow{3}{*}{2} & Analysis & 27.90 & 2.64 & 29.81 & 2.82 & 46.98 & 4.44 \\  & Test & 57.04 & 5.39 & 25.81 & 2.44 & 47.31 & 4.47 \\  & Error & & \(-\)51\% & & 15\% & & \(-\)0.7\% \\ \hline \multirow{3}{*}{3} & Analysis & 15.85 & 1.50 & 29.80 & 2.82 & 23.95 & 2.26 \\  & Test & 25.32 & 2.39 & 33.16 & 3.14 & 29.69 & 2.81 \\ \cline{1-1}  & Error & & \(-\)37\% & & \(-\)10\% & & \(-\)19\% \\ \hline \end{tabular}
\end{table} 
Table 8: PSD response before model correction. Figure 13: _Cont._