# Mechanical Structure Design and Experimental Study of Gamma-ray Monitor for Small Satellite Payload
## 4 Simulation and Experimental Results
### Dynamical Analysis
#### 4.2.2 Sinusoidal Vibration Analysis  
The sinusoidal vibration analysis model is consistent with the model of modal analysis. The damping ratio of the product structure is taken as the empirical value of 0.03, and the test conditions listed in Table 3 are used as the load input. The excitation frequency of the satellite engine is generally less than 100 Hz. In order to understand the dynamic performance of the model under this excitation, sinusoidal vibration analysis is carried out. The acceleration response curves obtained by FEM and test are shown in Figure 11.  
From comparison of the finite element analysis and experimental data, the relative error of the acceleration amplification factor \(Q\) is shown in Table 7. Combining with Table 7 and Figure 11, it can be found that the amplification factors in X, Y and Z directions of the test are consistent with the trends of the finite element analysis results. The overall excitation curve of the test is consistent with the FEM curve, there is no obvious peak, and the amplification factor of the acceleration response is also within the reasonable range of engineering requirements.  
After the identification level sinusoidal vibration test, the novel GRM must be subjected to the 0.5 g sinusoidal characteristic sweep frequency test. By comparing sweep frequency results before and after the sinusoidal vibration test, it is verified whether the structure is damaged under the excitation of sinusoidal vibration conditions. The results are shown in Figure 10.  
From the sinusoidal characteristic sweep frequency of each measuring point in X, Y and Z directions in Figure 10, it can be seen that the sweep frequency curves of each measuring point before and after the sinusoidal vibration test are consistent. Before and after the identification level sinusoidal vibration experiment, the frequency of the first order main frequency in X and Y directions does not change, and the drift value of the  
Figure 10: Plots of characteristic swept spectral lines before and after the sinusoidal characteristic sweep frequency test in X, Y, and Z directions for each measurement point: (**a**) Measurement point 1 in X-direction. (**b**) Measurement point 2 in X-direction. (**c**) Measurement point 3 in X-direction. (**d**) Measurement point 1 in Y-direction. (**e**) Measurement point 2 in Y-direction. (**f**) Measurement point 3 in Y-direction. (**g**) Measurement point 1 in Z-direction. (**h**) Measurement point 2 in Z-direction. (**i**) Measurement point 3 in Z-direction.  
first order main frequency in Z direction is less than 5.0%. Under sinusoidal excitation, the structure can be kept intact, indicating that the strength of the structure design meets the requirements under low frequency.  
Figure 11: Comparison of acceleration response curve between theoretical analysis and experimental test: (**a**) Acceleration response curve of theoretical analysis in X-directional. (**b**) Acceleration response curve of experimental test in X-directional. (**c**) Acceleration response curve of theoretical analysis in Y-direction. (**d**) Acceleration response curve of experimental test in Y-direction. (**e**) Acceleration response curve of theoretical analysis in Z-directional. (**f**) Acceleration response curve of experimental test in Z-directional.