## 4 Seismic Response Analysis of Isolated Structure Considering Negative Stiffness
### Seismic Response
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Seismic** \\ **Wave** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Peak Value** \\ **of Seismic** \\ **Wave** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Maximum Floor Acc(m/s\({}^{2}\))** \\ **of Seismic** \\ **Inkb** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Acc Response** \\ **Deviation Rate** \\ \end{tabular} } & \multicolumn{2}{c}{\
\begin{tabular}{c} **Maximum Displacement of** \\ **Isolation Layer (mm)** \\ \end{tabular} } & \multicolumn{2}{c}{
\begin{tabular}{c} **Displacement** \\ **Response** \\ **Deviation Rate** \\ \end{tabular} } \\ \cline{3-10}  & & & **LRB** & **NSD** & **DNSD** & & **LRB** & **NSD** & **DNSD** & **Deviation Rate** \\ \hline EL Centro & \(0.3\) g & \(2.01\) & \(1.90\) & \(1.58\) & \(-16.84\)\% & \(81\) & \(94\) & \(65\) & \(-30.85\)\% \\  & \(0.4\) g & \(2.70\) & \(2.63\) & \(2.27\) & \(-13.69\)\% & \(142\) & \(152\) & \(120\) & \(-21.05\)\% \\  & \(0.5\) g & \(3.19\) & \(2.77\) & \(2.68\) & \(-3.25\)\% & \(207\) & \(204\) & \(169\) & \(-17.16\)\% \\  & \(0.6\) g & \(4.27\) & \(3.62\) & \(3.13\) & \(-13.54\)\% & \(274\) & \(261\) & \(220\) & \(-15.71\)\% \\ \hline PAS-180 & \(0.3\) g & \(2.27\) & \(2.56\) & \(1.66\) & \(-35.16\)\% & \(156\) & \(160\) & \(126\) & \(-21.25\)\% \\  & \(0.4\) g & \(3.21\) & \(2.96\) & \(2.64\) & \(-10.81\)\% & \(226\) & \(226\) & \(200\) & \(-11.50\)\% \\  & \(0.5\) g & \(4.15\) & \(3.42\) & \(2.98\) & \(-12.87\)\% & \(297\) & \(289\) & \(261\) & \(-9.69\)\% \\  & \(0.6\) g & \(4.85\) & \(3.61\) & \(3.52\) & \(-2.49\)\% & \(366\) & \(347\) & \(318\) & \(-8.36\)\% \\ \hline SBA-042 & \(0.3\) g & \(2.90\) & \(3.13\) & \(2.92\) & \(-6.71\)\% & \(175\) & \(186\) & \(160\) & \(-13.98\)\% \\  & \(0.4\) g & \(3.85\) & \(3.82\) & \(3.43\) & \(-10.21\)\% & \(258\) & \(266\) & \(237\) & \(-10.90\)\% \\  & \(0.5\) g & \(4.71\) & \(4.48\) & \(4.07\) & \(-9.15\)\% & \(344\) & \(339\) & \(308\) & \(-9.14\)\% \\  & \(0.6\) g & \(5.46\) & \(5.04\) & \(4.75\) & \(-5.75\)\% & \(429\) & \(409\) & \(375\) & \(-8.31\)\% \\ \hline REN1 & \(0.3\) g & \(1.43\) & \(1.35\) & \(1.29\) & \(-4.44\)\% & \(81\) & \(86\) & \(75\) & \(-12.79\)\% \\  & \(0.4\) g & \(1.71\) & \(1.80\) & \(1.67\) & \(-7.22\)\% & \(118\) & \(132\) & \(114\) & \(-13.64\)\% \\  & \(0.5\) g & \(2.11\) & \(2.53\) & \(2.07\) & \(-18.18\)\% & \(156\) & \(176\) & \(157\) & \(-10.80\)\% \\  & \(0.6\) g & \(2.74\) & \(2.90\) & \(2.87\) & \(-1.03\)\% & \(198\) & \(243\) & \(189\) & \(-22.22\)\% \\ \hline REN2 & \(0.3\) g & \(1.41\) & \(1.45\) & \(1.21\) & \(-16.55\)\% & \(69\) & \(72\) & \(64\) & \(-11.11\)\% \\  & \(0.4\) g & \(1.80\) & \(1.90\) & \(1.73\) & \(-8.95\)\% & \(99\) & \(107\) & \(94\) & \(-12.15\)\% \\  & \(0.5\) g & \(2.61\) & \(2.44\) & \(2.31\) & \(-5.33\)\% & \(142\) & \(160\) & \(127\) & \(-20.63\)\% \\  & \(0.6\) g & \(3.28\) & \(2.93\) & \(2.67\) & \(-8.87\)\% & \(189\) & \(220\) & \(168\) & \(-23.64\)\% \\ \hline Average response & & & & & \(-10.55\)\% & & & & \(-15.24\)\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Summary of time history results under the action of local seismic waves (NSD vs. DNSD). Figure 21: Time-history comparison of bottom shear response among three models under different earthquake waves at a peak of 0.6 g. (**a**) Time history of shear response of ground floor under 0.6 g peak of EL wave. (**b**) Time history of shear response of ground floor under 0.6 g peak of PAS wave. (**c**) Time history of shear response of ground floor under 0.6 g peak of SBA wave. (**d**) Time history of shear response of ground floor under 0.6 g peak of REN1 wave. (**e**) Time history of shear response of ground floor under 0.6 g peak of REN2 wave. The comparison of floor accelerations of LRB, NSD, and DNSD under the peak inputs of 0.3 g and 0.6 g of five seismic waves is shown in Figures 23 and 24, respectively.