## 2 The Basic Theory of Shock Response Prediction
The phase of the structural response is very close to that of the loading signal. Therefore, the effect of \(K_{i}\) on the response prediction is usually ignored. The complex spacecraft structure contains a variety of structural forms. According to the hybrid FE-SEA theory, the structure can be divided into different subsystems, according to the modal characteristics of each part. The acceleration response of the subsystem with higher modal density has statistical characteristics when it is exposed to the shock load. The statistic characteristics can be processed by the concept of statistical average, while the subsystem with sparse modal density cannot be processed accurately. Therefore, the average value of the statistical energy of all subsystems of the overall spacecraft structure cannot be inferred by the modal density in the frequency range alone, nor can the overall reliable response result be obtained by the finite element method alone. In this case, the most reasonable method is to carry out hybrid FE-SEA modeling for complex structures. The subsystem with higher modal density is the SEA system, and the subsystem with sparse modal density is the FE system. In this paper, the hybrid FE-SEA model of spacecraft structure is established. Based on the FE-SEA model, the acceleration frequency response of the structure in each frequency band is calculated. In the hybrid FE-SEA method, diffuse reflection means the reverberant energy field after multiple reflections. The direct field only satisfies the output displacement field on the deterministic boundary, and the energy can be radiated out through the direct field subsystem. The function of reverberation field is to superimpose the boundary conditionsof reverberation field and direct field linearly. The deterministic and stochastic boundary conditions are satisfied simultaneously [23; 24]. The dynamic equation of subsystem boundary can be written as follows:  
\[\mathbf{D}_{\rm dir}^{(b)}\mathbf{q}^{(b)}=\mathbf{f}_{\rm ext}^{(b)}+\mathbf{f}_{\rm rev}^{(b)} \tag{5}\]  
where \(\mathbf{D}_{\rm dir}^{(b)}\) is the dynamic stiffness matrix of direct field, which is used to solve the displacement on the definite boundary, \(\mathbf{f}_{\rm rev}^{(b)}\) is the reverberation force generated by reverberation field energy, and \(\mathbf{f}_{\rm ext}^{(b)}\) is the external load. After coupling, only considering the effect of the  
Figure 2: Acceleration response analysis of a single-degree-of-freedom system under sinusoidal shock loading. external force of the deterministic subsystem on the deterministic subsystem, the dynamic equation of the deterministic subsystem can be shown as follows:  
\[\mathbf{D}_{\text{tot}}\mathbf{q}=\mathbf{f}_{\text{ext}}+\sum_{m}\mathbf{f}_{\text{rev}}^{(b)} \tag{6}\]  
where \(\mathbf{D}_{\text{tot}}=\mathbf{D}_{d}+\sum\limits_{m}\mathbf{D}_{\text{dir}}^{(b)}\), \(\mathbf{D}_{d}\) is the dynamic stiffness matrix of the deterministic subsystem, \(\mathbf{q}\) is a deterministic generalized coordinate, and \(\mathbf{f}_{\text{ext}}\) is the sum of the external loads. The set average of Equation (6) is solved. The response cross-spectrum can be given as follows:  
Figure 1:0  
where \(\mathbf{S}_{\text{ff,ext}}\) is the cross-spectrum of external load, and \(\mathbf{S}_{\text{ff,rev}}^{(b)}\) is the cross-spectrum of blocked diffuse reverberant force. The set average related to the blocking force \(\mathbf{S}_{\text{ff,rev}}^{(b)}\) in the reverberation field can be obtained from the reciprocity between the direct field and the reverberation field. In a diffuse reverberation field, because of the relationship between the blocking force of the stochastic subsystem in the reverberation field and the uncertainty of the system, the set related to \(\mathbf{S}_{\text{ff,rev}}^{(b)}\) tends to the following values:  
Figure 1:1  
where \(\alpha_{\text{b}}=\frac{4E_{b}}{\omega\pi\eta_{b}}\) is the proportional constant related to the reverberation field amplitude, and \(E_{b}\) is the diffuse reverberant energy.