## 2 Numerical Analysis
### Results of Numerical Analysis
#### 2.5.2 Acceleration and Inter-Story Displacement  
Tables 7 and 8 respectively present the average absolute accelerations and inter-story displacements of both story isolation FEA model and non-isolated FEA model under earthquake excitations with different PGAs. The response's decreasing ratios of story isolation model compared to the non-isolated model are also presented. Note: The decreasing ratio = (response of the story isolation model \(-\) response of the non-isolated model)/response of non-isolated model. The response means acceleration or displacement in this study.  
The results show that the insert of the isolation layer significantly decreases the acceleration values of different stories above the first story. The acceleration values of the story isolation model range from 0.149 to 0.418 g, while those of the non-isolated model increase from 0.362 to 1.088 g. The inserting of the isolation layer produces a significant seismic damping effect on the acceleration response of stories above the isolation layer as the decreasing ratios of acceleration values are generally more than 61% regardless of PGAs (Figure 8). The above results also can be illustrated in Figure 9 where the variations of story acceleration from base to the top floor are shown when the PGAs are 0.30 g and 0.40 g.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Story**} & \multicolumn{2}{c}{**0.30 g**} & \multicolumn{2}{c}{**0.40 g**} \\ \cline{2-5}  & \multicolumn{1}{c}{**Story Isolation**} & \multicolumn{1}{c}{**Non-Isolated Model**} & \multicolumn{1}{c}{**Isolation Model**} & \multicolumn{1}{c}{**Non-Isolated Model**} \\ \cline{2-5}  & \multicolumn{1}{c}{**Model (g)**} & \multicolumn{1}{c}{**Model (g)**} & \multicolumn{1}{c}{**Model (g)**} & \multicolumn{1}{c}{**Model (g)**} \\ \hline
7 & 0.170 & 0.702 & 0.291 & 1.088 \\
6 & 0.165 & 0.597 & 0.255 & 1.011 \\
5 & 0.166 & 0.531 & 0.229 & 0.885 \\
4 & 0.167 & 0.512 & 0.220 & 0.794 \\
3 & 0.164 & 0.461 & 0.209 & 0.712 \\
2 & 0.158 To demonstrate the story displacement response, Table 8 shows the inter-story displacements of the non-isolated model and the story isolation model, and Figure 10 presents the decreasing ratios of inter-story displacement values when the isolation layer was applied. The results show that both the displacement and its angle in the story isolation model (either above or below the isolation layer) were significantly less than those in the non-isolated model regardless of PGA. The decreasing ratio ranges from 70.3% up to 91.5% (PGA = 0.3 g) and from 65.1% up to 92.5% (PGA = 0.40 g). In addition, the inter-story displacement value decreases with increasing story height, regardless of the structure model type or PGA value. For the isolation model, the increase of the story displacement is less  
Figure 8: The decreasing ratio of story acceleration values in the story-isolated structure after being subjected to earthquakes at peak acceleration (PGA) of 0.30 g or 0.40 g compared to the non-isolated structure (numerical).  
Figure 9: Comparison of story acceleration between isolation model and non-isolated model at PGAs of (**a**) 0.30 g and (**b**) 0.40 g.  
compared to the non-isolated model. The stories above the isolation layer almost horizontally move, while the stories in the non-isolated model increase significantly in their horizontal displacements, as shown in Figure 11.