## 2 Validation of Finite Element Simulation Methodology
### Verification of Test Results and Finite Element Results  
For isolated structures, the first three modes of vibration predominantly govern the dynamic response. The finite element analysis and experimental results exhibit a favorable agreement in the periods of the first two translational modes. A comparative analysis of modal frequencies is presented in Table 1, and the mode shapes of the finite element model are shown in Figure 4.  
The seismic isolation structure was subjected to tri-directional input by using the artificial ground motion acceleration of the Safe Shutdown Earthquake (SL-2) level, which represents the ultimate safety seismic motion. The peak ground acceleration (PGA) of the prototype ground motion corresponding to the SL-2 level is 0.3 g. A comparative analysis was conducted between the finite element results and the experimental data. Figure 5  
Figure 3: Model: (**a**) Seismic isolation test model. (**b**) Finite element model of base isolation structure factory building. (**c**) Mechanical properties of LRB.  
presents a comparison of the hysteretic curves for the lead rubber bearing (LRB) under the same conditions, as obtained from the finite element model and the experimental model. The LRB is assigned horizontal bilinear hysteresis model through the elements, resulting in a more robust finite element hysteretic curve that exhibits a significantly more realistic response. However, the bilinear hysteresis model cannot fully capture the dynamic behavior of the horizontal stiffness of the LRB, resulting in errors between the test results of the hysteresis curve and the finite element results.  
Figure 6 compares the acceleration-time-history curves of the experimental and finite element models. Subfigures (a) and (b) depict the horizontal acceleration comparisons at the first floor and the top floor, respectively, where the first-floor acceleration also represents the acceleration above the isolation layer. As illustrated in the figure, the waveforms and overall trends of the time-history curves from both models exhibit a high degree of consistency, with closely matched peak values. There are differences between the two acceleration-time-history curves around 4 s. This is attributed to the peak of ground motion acceleration occurring at approximately this time. During this period, the metal counterweights in the test model collide with each other, leading to a sudden increase in acceleration. Nevertheless, this phenomenon was not considered in the finite element model.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Mode**} & \multicolumn{2}{c}{**Test Result**} & \multicolumn{2}{c}{**Finite Element Model of Test Structure**} & \multirow{2}{*}{**Error**} \\ \cline{2-2} \cline{4-5}  & **Frequency (Hz)** & **Direction** & **Frequency (Hz)** & **Direction** & \\ \hline
1 & 2.30 & Y & 2.32 & Y & 0.8\% \\
2 & 2.33 & X & 2.34 & X & 0.4\% \\
3 & 2.42 & Twist & 2.39 & Twist & \(-1.3\%\) \\
4 & 12.00 & Y & 16.7 & Y & 28.1\% \\
5 & 26.00 & X & 25.68 & X & \(-1.3\%\) \\
6 & 30.50 & Z & 44.29 & Z & 31.1\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: Modal comparison between shaking table test model and finite element model.  
Figure 4: Mode shapes of finite element model.