## 4 Results and Discussion
### Vibration Isolation Performance  
Notwithstanding the metal lattice structure's operation in the linear elastic regime, significant variations are observed in its dynamic stiffness and damping behavior when subjected to vibrational loads compared to shock loading scenarios. Through swept-frequency excitation testing of the metal lattice vibration isolation system, the resonant frequency is determined to be 73.55 Hz with a corresponding response peak of 53.5384, as derived from the vibration transmissibility curve. Experimental characterization yields a stiffness of 6.031 \(\times\) 10\({}^{6}\) N/m and a damping coefficient of 243.49 N\(\cdot\)s/m for the metal lattice structure. The vibration transmissibility curves for the LS, CS-6 mm, and CS-8 mm vibration isolation systems were calculated, as shown in Figure 13a. Through swept-frequency testing of the shaking table, the vibration transmissibility curves for the LS, CS-6 mm, and CS-8 mm systems were obtained, as shown in Figure 13b. Table 4 shows the theoretical and experimental results of sweep-frequency responses. The LS vibration isolation system demonstrates the highest resonance peak (53.60), followed by the CS-6 mm (32.41) and CS-8 mm (26.28) systems, with the composite systems achieving up to 50.97% peak attenuation. In addition, the natural frequencies remain virtually unchanged. Thus, the introduction of the polyurea damping structure enhanced the vibration isolation effect. The system's damping ratio and damping coefficient were calculated using Equation (4) and subsequently compared with theoretical values, as summarized in Table 5. The experimental results are consistent with the trend of the theoretical solution but are smaller than the theoretical results. This might be because the damping capacity was insufficient because of the excessively small vibration displacement. However, after the introduction of the polyurea damping structure, the damping coefficient and damping ratio of the system were significantly enhanced. The damping coefficient of the CS-8 mm vibration isolation system was the largest, increasing from 486.98 N\(\cdot\)s/m of the LS vibration isolation system to 995.47 N\(\cdot\)s/m, an increase of 104.42%. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Type**} & \multicolumn{2}{c}{**Theoretical Results**} & \multicolumn{2}{c}{**Experimental Results**} \\  & **Natural Frequency/Hz** & **Peak Value** & **Natural Frequency/Hz** & **Peak Value** \\ \hline LS & 73.55 & 53.54 & 73.55 & 53.60 \\ CS-6 mm & 74.50 & 20.59 & 73.63 & 32.41 \\ CS-8 mm & 74.60 & 15.76 & 73.63 & 26.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Theoretical and experimental results of sweep-frequency responses. Figure 13: Vibration transmissibility curves of the three vibration isolation systems: (**a**) theoretical results; (**b**) experimental results. The research focus of this paper lies in exploring a method that can be applied in extreme environments to enhance the damping performance of the system while ensuring a large load-bearing capacity. The response characteristics of the vibration isolation system under vibration and shock are related to its stiffness, damping ratio, and load mass. The load mass adopted in this paper is 56.54 kg. In the existing traditional vibration isolation research of lattice structures, in references [6,37], the load masses are 1 kg and 90 g, respectively, which obviously increases the damping ratio of the system and thereby reduces the peak value of vibration transmissibility. Meanwhile, their materials are both acrylonitrile butadiene styrene (ABS), which has poor radiation resistance and anti-aging ability. Under the shock excitation, the maximum response peak decay is not significant. This is because the peak of the shock response is greatly influenced by the stiffness, while the damping ratio has a relatively small effect on the peak of the shock response.