# Enhancing Friction Pendulum Isolation Systems Using Passive and Semi-Active Dampers
## 5 Results and Analysis
### Performance Discussion
Valley} & Non-isolated & 1.000 & 1.000 & - & - & 1.000 & 1.000 & 1.000 & 1.000 & 0.833 \\  & FPS\({}_{\mu=0.05}\) & 0.864 & 0.763 & 0.069 & 0.019 & 0.441 & 0.486 & 0.418 & 0.310 & 0.511 \\  & FPS+VD & 0.868 & 0.760 & 0.052 & 0.017 & 0.432 & 0.479 & 0.390 & 0.298 & 0.504 \\
6.5 Mw & FPS+SD\({}_{Phase}\) & 0.897 & 0.761 & 0.069 & 0.023 & 0.460 & 0.453 & 0.426 & 0.285 & 0.517 \\ USA & FPS+SD\({}_{Energy}\) & 0.855 & 0.773 & 0.065 & 0.016 & 0.487 & 0.515 & 0.415 & 0.330 & 0.530 \\  & FPS\({}_{\mu=0.20}\) & 0.953 & 1.288 & 0.110 & 0.011 & 1.656 & 1.484 & 2.459 & 2.255 & 1.191 \\ \hline \multirow{6}{*}{Corinth} & Non-isolated & 1.000 & 1.000 & - & - & 1.000 & 1.000 & 1.000 & 1.000 & 0.833 \\  & FPS\({}_{\mu=0.05}\) & 0.352 & 0.177 & 0.973 & 0.114 & 0.140 & 0.123 & 0.166 & 0.049 & 0.288 \\ Corinth & FPS+VD & 0.346 & 0.176 & 0.766 & 0.113 & 0.132 & 0.123 & 0.160 & 0.046 & 0.279 \\
6.6 Mw & FPS+SD\({}_{Phase}\) & 0.345 & 0.178 & 0.820 & 0.114 & 0.148 & 0.127 & 0.158 & 0.046 & 0.294 \\ GREECE & FPS+SD\({}_{Energy}\) & 0.303 & 0.185 & 0.618 & 0.087 & 0.157 & 0.140 & 0.113 & 0.044 & 0.260 \\  & FPS\({}_{\mu=0.20}\) & 0.332 & 0.267 & 0.597 & 0.067 & 0.258 & 0.248 & 0.124 & 0.077 & 0.327 \\ \hline \multirow{6}{*}{Northridge} & Non-isolated & 1.000 & 1.000 & - & - & 1.000 & 1.000 & 1.000 & 1.000 & 0.833 \\  & FPS\({}_{\mu=0.05}\) & 0.597 & 0.407 & 1.156 & 0.239 & 0.248 & 0.181 & 0.766 & 0.202 & 0.473 \\
6.69 Mw & FPS+VD & 0.596 & 0.405 & 1.126 & 0.227 & 0.231 & 0.176 & 0.684 & 0.180 & 0.461 \\ USA & FPS+SD\({}_{Phase}\) & 0.588 & 0.392 & 0.863 & 0.152 & 0.245 & 0.176 & 0.340 & 0.116 & 0.418 \\  & FPS+SD\({}_{Energy}\) & 0.602 & 0.408 & 0.759 & 0.133 & 0.268 & 0.185 & 0.294 & 0.115 & 0.415 \\  & FPS\({}_{\mu=0.20}\) & 0.607 & 0.514 & 0.581 & 0.098 & 0.357 & 0.370 & 0.274 & 0.180 & 0.464 \\ \hline \multirow{6}{*}{El Centro} & Non-isolated & 1.000 & 1.000 & - & - & 1.000 & 1.000 & 1.000 & 1.000 & 0.833 \\  & FPS\({}_{\mu=0.05}\) & 0.338 & 0.221 & 0.827 & 0.190 & 0.125 & 0.126 & 0.234 & 0.065 & 0.294 \\  & FPS+VD & 0.333 & 0.221 & 0.803 & 0.190 & 0.117 & 0.125 & 0.230 & 0.062 & 0.286 \\
6.9 Mw & FPS+SD\({}_{Phase}\) & 0.344 & 0.220 & 0.824 & 0.175 & 0.129 & 0.132 & 0.197 & 0.057 & 0.296 \\ USA & FPS+SD\({}_{Energy}\) & 0.312 & 0.227 & 0.617 & 0.143 & 0.145 & 0.147 & 0.155 & 0.057 & 0.266 \\  & FPS\({}_{\mu=0.20}\) & 0.392 & 0.279 & 0.465 & 0.090 & 0.218 & 0.240 & 0.116 & 0.073 & 0.302 \\ \hline \multirow{6}{*}{Irpinia} & Non-isolated & 1.000 & 1.000 & - & - & 1.000 & 1.000 & 1.000 & 1.000 & 0.833 \\  & FPS\({}_{\mu=0.05}\) & 0.231 & 0.204 & 0.239 & 0.049 & 0.161 & 0.189 & 0.131 & 0.054 & 0.198 \\ \cline{1-1}  & FPS+VD & 0.243 & 0.213 & 0.251 & 0.049 & 0.159 & 0.199 & 0.132 & 0.057 & 0.204 \\
6.9 Mw & FPS+SD\({}_{Phase}\) & 0.242 & 0.218 & 0.241 & 0.047 & 0.163 & 0.205 & 0.124 & 0.057 & 0.205 \\ ITALY & FPS+SD\({}_{Energy}\) & 0.261 & 0.230 & 0.206 & 0.038 & 0.182 & 0.219 & 0.107 & 0.059 & 0.213 \\  & FPS\({}_{\mu=0.20}\) & 0.510 & 0.511 & 0.200 & 0.030 & 0.455 & 0.502 & 0.315 & 0.268 & 0.439 \\ \hline \multirow{6}{*}{Iwate} & Non-isolated & 1.000 & 1.0 stroke saturation under large ground motions, and showing low friction performance under low ground motions. From Figure 18a,b, it can be observed that the high-friction FPS cannot cope with low ground motions. From Figure 18c,d, it can be observed that small plate sizes for the semi-active versions can also be really effective. Additionally, for the low-friction single FPS and the FPS+VD, for small plate sizes, the performance is even worse than the one of the non-isolated structure. Table 5 summarizes the optimization function values and the improvement obtained for each isolation system with the same concave plate size (\(R_{eff}\)) under the serviceability and design earthquake. The semi-active isolators are effective for both earthquakes while the FPS+VD and the low-friction FPS are only effective for the serviceability earthquake and the high-friction FPS only works for the design earthquake.