# 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  
On the basis of modal analysis, the damping ratio was taken as 0.03, and the test conditions listed in Table 4 were used as load input to calculate the response of the product under random excitation in X, Y and Z directions. In the random vibration test, the excitations of each frequency component acts simultaneously on the satellite structure at any time, so it is impossible to predict its instantaneous vibration variation law. Generally, statistics such as root mean square, cumulative root mean square and PSD curve are used to study the random vibration of the satellite structure [35]. The acceleration power spectral density curves of FEM and experiment are shown in Figure 12. \begin{table}
\begin{tabular}{l 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}  & & **g** & **Magnification** & **g** & **Magnification** & **g** & **Magnification** \\ \hline \multirow{2}{*}{1} & Analysis & 12.67 & 1.01 & 13.27 & 1.06 & 12.91 & 1.03 \\  & Test & 12.84 & 1.03 & 14.5 & 1.16 & 13.39 & 1.07 \\  & Error & & 1.3\% & & 8.5\% & & 3.6\% & \\ \hline \multirow{2}{*}{2} & Analysis & 12.75 & 1.02 & 13.25 & 1.06 & 12.82 & 1.03 \\  & Test & 12.82 & 1.03 & 13.51 & 1.08 & 12.82 & 1.03 \\  & Error & & 0.5\% & & 1.9\% & & 0\% & \\ \hline \multirow{2}{*}{3} & Analysis & 12.59 & 1.01 & 13.27 & 1.06 & 12.69 & 1.015 \\  & Test & 13.46 & 1.08 & 13.47 & 1.077 & 12.71 & 1.02 \\  & Error & & 6.5\% & & 1.5\% & & 0.1\% & \\ \hline \end{tabular}
\end{table} 
Table 7: Comparison of theoretical analysis and experimental test acceleration response data. Figure 12: _Cont._The acceleration PSD curve of measuring points 1-3 is shown in Figure 12. The first peak in X direction is 755 Hz and 732 Hz in test and finite element analysis, respectively; the first peak in Y direction is 425 Hz and 420 Hz in test and finite element analysis, respectively; the first peak in Z direction is 547 Hz and 615 Hz in test and finite element analysis respectively; and the fundamental frequency error of each measuring point direction meets the engineering requirements. The peak and valley number of PSD in 200-1000 Hz is basically consistent with the experimental curve. There is an obvious difference between the theoretical curve and the experimental curve of PSD in the high frequency band of 1000-2000 Hz, and the reasons for the deviation are analyzed as follows:  
1. The deviation of finite element modeling. In order to simplify the finite element calculation, the tie constraint and MPC algorithm are used to simulate the screw connection, so that the stiffness of the connection area is deviated from the actual stiffness. This is also the reason for the deviation between the natural frequencies obtained by the analysis of the test in each stage. Figure 12: Comparison of theoretical analysis and experimental test PSD response curves: (**a**) X-directional PSD response curve of theoretical analysis. (**b**) X-directional PSD response curve of experimental test. (**c**) Y-directional PSD response curve of theoretical analysis. (**d**) Y-directional PSD response curve of experimental test. (**e**) Z-directional PSD response curve of theoretical analysis. (**f**) Z-directional PSD response curve of experimental test. 2. Uncertainty of modal damping selection. In the process of finite element simulation and calculation, the damping value was adopted the empirical value of 0.03, which deviates from the actual damping value of the model. 3. Test error. In the test stage, there is a coupling effect in the transmission process of random excitation applied by the vibration platform. There are deviations between the idealized treatment of factors (such as inter-part friction and inter-part clearance) and the random vibration test. 4.