## 4 Calculation Results and Experimental Validation
### Experimental Validation of Isolation Effect  
The isolation bearing process based on optimized parameters is shown in Figure 7. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Parameters**} \\ \(h_{1}\) (mm) & \(h_{2}\) (mm) & \(l\) (mm) & \(r\) (mm) & K\({}_{V}\) (N/mm) & K\({}_{H}\) (N/mm) \\ \hline
8 & 13 & 22 & 14 & 259.80 & 184.77 \\
8 & 15 & 24 & 16 & 229.21 & 170.40 \\
8 & 17 & 26 & 18 & 198.75 & 155.05 \\
10 & 13 & 24 & 18 & 223.98 & 348.67 \\
10 & 15 & 26 & 14 & 179.38 & 133.93 \\
10 & 17 & 22 & 16 & 249.98 & 173.71 \\
12 & 13 & 26 & 16 & 182.70 & 147.06 \\
12 & 15 & 22 & 18 & 244.25 & 175.81 \\
12 & 17 & 24 & 14 & 206.34 & 290.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results of sensitivities of parameters. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Vertical Stiffness**} & \multicolumn{4}{c}{**Horizontal Stiffness**} \\  & \(h_{1}\) (mm) & \(h_{2}\) (mm) & \(l\) (mm) & \(r\) (mm) & & \(h_{1}\) (mm) & \(h_{2}\) (mm) & \(l\) (mm) & \(r\) (mm) \\ \hline \(K_{1 ij}\) & 687.76 & 666.47 & 754.03 & 645.51 & \(K_{1j}\) & 510.21 & 680.50 & 534.29 & 608.98 \\ \(K_{2j}\) & 653.34 & 652.84 & 659.52 & 661.89 & \(K_{2j}\) & 656.31 & 480.14 & 809.35 & 491.16 \\ \(K_{3j}\) & 633.29 & 655.07 & 560.83 & 666.98 & \(K_{3j}\) & 613.16 & 619.03 & 436.04 & 679.53 \\ \(R_{j}\) & 18.16 & 4.54 & 64.40 & 7.16 & \(R_{j}\) & 48.70 & 66.79 & 124.44 & 62.79 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Range analysis of each parameter. Figure 7: The isolation bearing. The vibration table experiment for the structure equipped with isolation bearings is illustrated in Figure 8.  
First, the vertical impact load \(\mathbf{p}(t)\) was applied to test the acceleration-time curves and the acceleration-transmission ratio-time curves at the center node of the top surface of the isolated object. One test was performed with the optimized devices, while another test was conducted with conventional devices, as shown in Figures 9 and 10. The equation used was  
\[p(t)= \begin{cases}0.3g\sin\frac{\pi}{\Pi}t&(t\leq 11\text{ ms})\\ 0&(t>11\text{ ms})\end{cases}  \tag{10}\]  
where \(\mathbf{g}\) represents the acceleration due to gravity, as shown in Equation (10). Based on Figures 9 and 10, it can be observed that before optimization, the maximum vertical acceleration at the center node of the top surface of the isolated object was 4.77 m/s\({}^{2}\), with a maximum acceleration-transmission ratio of 161.98%. This indicates a significant amplification of the acceleration at the top surface of the isolated object, suggesting that the conventional device was ineffective in reducing vibrations. After optimization, the maximum vertical acceleration at the center node of the top surface of the isolated object decreased to 1.87 m/s\({}^{2}\), with a maximum acceleration-transmission ratio of 63.30%. In this case, the acceleration at the top surface of the isolated object was less than that at the bottom of the structure, demonstrating that the optimized device effectively reduced vibrations. Figure 8: Test experiment on isolation effect. Figure 9: Acceleration versus time curves under the vertical impact load. Subsequently, the horizontal harmonic load was applied to test the acceleration-time curves at the center node of the top surface of the isolated object. The first curve represents the acceleration curve at the base of the structure, the second curve represents the acceleration curve with conventional devices installed, and the third curve represents the acceleration curve with optimized devices installed. The acceleration-response curves for harmonic loads with frequencies of 0.5 Hz, 1 Hz, 5 Hz, and 10 Hz are shown in Figures 11-14, respectively. Based on Figures 11-14, it can be observed that under horizontal harmonic loads of 0.5 Hz, 1 Hz, 5 Hz, and 10 Hz, the maximum acceleration-transmission ratios of the isolated object with conventional devices installed are 73.2%, 36.1%, 88.9%, and 65.4%, respectively.