## 4 Results and Discussion
### Shock Resistance Performance  
A semi-sinusoidal wave signal excitation with a peak of 1 g and a duration of 6 ms was applied to the vibration isolation system consisting of two metal lattice structures and the load mass \(m\). The resonance peak derived from spectral analysis of the system's response signal was utilized to calculate the dynamic stiffness of the metal lattice structure. The damping coefficient was determined using the free decay oscillation method [35; 36]. The calculated dynamic stiffness and damping coefficient of the metal lattice structure were 5.7214 \(\times\) 10\({}^{6}\) N/m and 1051.8 N\(\cdot\)s/m, respectively. The shock response curves of the metal lattice structure (LS) and metal lattice-polyurea parallel composite structures under the pre-compression displacements of 6 mm and 8 mm (CS-6 mm and CS-8 mm) vibration isolation systems, respectively, were numerically calculated using a semi-sinusoidal wave signal excitation with a peak of 1 g and a duration of 6 ms, as shown in Figure 12a. The shock response curves of the three isolation systems, obtained from the corresponding shock experiments, are shown in Figure 12b. The acceleration response attenuation rates of the composite structures are both increased, with the CS-8 mm system exhibiting the most rapid attenuation. Table 2 shows the theoretical and experimental results of the shock responses. There is a certain error between the theoretical and the experimental results of the maximum peak value of the shock response of the LS system, which might be caused by the certain errors in calculating the stiffness and damping of the metal lattice structure. However, the error does not affect the analysis of the shock resistance performance of the composite structure after the introduction of the polyurea damping structure. The experimental results show that the maximum peak value of the shock response of CS-6 mm and CS-8 mm systems decrease by 18.3% and 18.5% compared with the LS system. The system's damping characteristics, including both damping ratio and damping coefficient, are experimentally determined through shock response analysis and subsequently compared with theoretical predictions, as summarized in Table 3.  
The comparative analysis reveals that the integration of the polyurea damping structure significantly enhances the damping performance of the composite vibration isolation system, with experimental results exceeding theoretical estimations. Particularly, the CS-6 mm and CS-8 mm systems exhibit 96.27% and 107.03% increases in damping coefficients, respectively, compared to the LS system. This observed discrepancy may stem from two principal mechanisms. Primarily, the polyurea material undergoes high-strain-rate deformation under shock loading, which activates molecular chain mobility and subsequent rupture of doubly coordinated hydrogen bonds between polyurea molecules. This bond dissociation process dissipates considerable energy, thereby enhancing the damping characteristics. Secondarily, inherent variations in both the peak magnitude and temporal duration of the shock excitation introduce measurement uncertainties in the shock response, consequently elevating the derived damping parameters (damping ratio and damping coefficient). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type** & **Theoretical Maximum** & **Experimental Maximum** \\  & **Response/(m/s\({}^{2}\))** & **Response/(m/s\({}^{2}\))** \\ \hline LS & 13.286 & 11.659 \\ CS-6 mm & 13.200 & 9.525 \\ CS-8 mm & 13.146 & 9.506 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Theoretical and experimental results of the shock responses. Figure 12: Shock response curves of the three vibration isolation systems (LS, CS-6 mm, and CS-8 mm represent the shock response curves of the metal lattice structure, the metal lattice–polyurea parallel composite structure with a pre-compression displacement of 6 mm, and the metal lattice–polyurea parallel composite structure with a pre-compression displacement of 8 mm, respectively.