## 3 Shock Experiment and Simulation Study of Spacecraft Structure
### Results and Discussion  
In this chapter, the shock response of the loading plate and the response plate of the spacecraft structure are obtained by the hybrid FE-SEA method. The \(SRS\) of calculation and experiment for the plate 1 are plotted in Figure 10. The \(SRS\) of the calculation and experiment for the other three response plates are shown in Figures 11-13, respectively. With the change of in frequency, the \(SRS\) curves of the four plate test results have a similar trend. The value shows an upward trend form, reaching the inflection point and the maximum at about 2500 Hz. At the same frequency band width, the values from plate 1 to plate 4 show a downward trend. The test results are consistent with the physical law of shock load transmission in the structure. By comparing the numerical and experimental data of the spacecraft structure, the rationality and sufficient accuracy of the proposed method in this paper are discussed. From Figures 10-13, it is shown that the numerical results are in good agreement with the experimental results. The maximum and inflection points of the two results are close. The evolution trend of the two curves with the increase of frequency are the same. In most frequency bands, the calculated results are within 6 dB of the experimental results. However, it is obvious that in some cases, the error of the calculation results is large, especially in some low-frequency bands. The finite element model of the structural cabin is established, and the traditional finite element is used to analyze the response of the structural cabin. In order to ensure the calculation accuracy of high frequency band, the grid size should meet the requirements of the modal analysis. The structure needs to be divided into at least 170,000 units. It is calculated every 10 \(\upmu\)s step, and it takes more than 24 h to calculate 10,000 \(\upmu\)s. The high-frequency band of the calculation results will be inaccurate, due to the high modal density. The new method is used to predict the shock response of the spacecraft cabin, which avoids  
Figure 9: The \(SRS\) result of spacecraft structures by hybrid FE-SEA method. the meshing of the plate structure. The same computer is used for the calculation, according to the frequency band based on the hybrid model. The above calculation results can be obtained in only a few minutes, which greatly improves the calculation efficiency. The calculation accuracy of high frequency band is also guaranteed. Figure 11: Shock responses of experiment and calculation for plate 2. Figure 10: Shock responses of experiment and calculation for plate 1.  
the response result of the plate is the average of the five sensors. Since the number of measurement points is limited, the average response of these measurement points will also bring errors. It can be found that the calculated results of plate 1 are more consistent with the experimental results than the other three plates. The calculated results of the plate 4 are the worst. It can be found that the farther the structure is from the shock source, the less consistent the calculated and experimental results are. In order to describe the above comparison results clearly, the coefficient \(E\) is constructed to represent the error, which is defined as follows:  
\[E=\frac{\sum_{f=f_{0}}^{f_{N}}|SRS_{c}(f)-SRS_{e}(f)|}{\sum_{f=f_{0}}^{f_{N}} SRS_{e}(f)} \tag{14}\]  
where \(SRS_{c}(f)\) and \(SRS_{e}(f)\) are the calculated \(SRS\) and the experimental \(SRS\), respectively. Obviously, the coefficient \(E\) is positive. The greater the coefficient \(E\), the greater the error. By using Equation (14), the coefficient \(E\) for the plate in Figures 10-13 can be calculated to be 0.179, 0.604, 0.596 and 0.697, respectively. This analysis shows that the error increases when the stress wave passes through the connecting structure. When the energy is transmitted from the shock source to the response plate, the more subsystems it passes through, the greater the prediction error of the response plate.