## 5 Numerical Simulations
In Figure 10, it can be seen that, compared to the uncontrolled case, the peak and RMS displacements of the base for the two control cases are significantly reduced. The control effect of the maximum passive control for the base displacement is much larger. For the maximum passive control case and the SHFLC case, the average reduction ratios of the peak base displacement under types A and B in Table 1 are 38.3% and 29.8%, respectively. For the passive control case and SHFLC case, the average reduction ratios of the RMS base displacement are 32.6% and 25.1%, respectively. However, it can be seen in Figure 11 that the max passive control can significantly amplify the peak and RMS floor acceleration for most of the selected earthquakes. Similarly, for the SHFLC case, the peak and RMS floor accelerations will be amplified for some of the selected earthquakes. For the maximum passive control case and SHFLC case, the average amplification ratios of peak floor acceleration are 27.8% and 3.7%, respectively. For the maximum passive control case, the average amplification ratio of RMS floor acceleration is 28.3%, while the average reduction ratio of the RMS floor acceleration \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Earthquake** & **Control Case** & \(J_{1}\) & \(J_{2}\) & \(J_{3}\) & \(J_{4}\) & \(J_{5}\) & \(J_{6}\) & \(J_{7}\) & \(J_{8}\) & \(J_{9}\) \\ \hline \multirow{3}{*}{C1} & Passive-max & 0.92 & 0.92 & 0.66 & 0.94 & 1.48 & 0.43 & 0.74 & 1.34 & **0.33** \\  & SHFLC & **0.74** & **0.74** & **0.60** & **0.75** & **1.40** & **0.33** & **0.71** & **1.20** & 0.28 \\ \hline \multirow{3}{*}{C2} & Passive-max & 0.94 & 0.98 & 0.81 & 1.12 & 1.29 & 0.40 & 0.81 & 0.72 & **0.45** \\  & SHFLC & **0.93** & **0.95** & **0.74** & **0.96** & **1.03** & **0.42** & **0.77** & **0.57** & 0.37 \\ \hline \multirow{3}{*}{C3} & Passive-max & 0.85 & **0.93** & **0.62** & **0.93** & 1.42 & 0.51 & **0.67** & 1.19 & **0.41** \\  & SHFLC & **0.81** & 0.97 & 0.83 & 0.97 & **1.17** & **0.33** & 0.89 & **0.97** & 0.35 \\ \hline \multirow{3}{*}{C4} & Passive-max & **0.90** & **0.89** & **1.06** & **1.00** & **0.95** & 0.45 & **1.00** & 0.85 & **0.39** \\  & SHFLC & 0.98 & **0.89** & 1.21 & 1.09 & 1.07 & **0.40** & 1.15 & **0.84** & 0.32 \\ \hline \multirow{3}{*}{D1} & Passive-max & 1.09 & 1.17 & **0.69** & 1.46 & 1.17 & 0.87 & 0.76 & 1.10 & 0.19 \\  & SHFLC & **0.89** & **0.91** & 0.90 & **0.94** & **0.89** & **0.52** & **0.86** & **0.77** & **0.23** \\ \hline \multirow{3}{*}{D2} & Passive-max & 1.29 & 1.32 & **0.39** & 1.60 & 1.37 & 0.97 & **0.42** & 1.22 & **0.41** \\  & SHFLC & **0.96** & **0.99** & 0.51 & **1.00** & **1.14** & **0.72** & 0.43 & **1.03** & 0.27 \\ \hline \multirow{3}{*}{D3} & Passive-max & **0.99** & 0.93 & **0.65** & **1.18** & 1.22 & 0.70 & **0.59** & 0.96 & **0.36** \\  & SHFLC & 1.03 & **0.80** & 0.75 & 1.27 & **1.12** & **0.55** & 0.69 & **0.81** & 0.27 \\ \hline \multirow{3}{*}{D4} & Passive-max & **0.78** & 0.83 & **0.52** & **0.83** & 1.39 & 0.91 & **0.55** & 1.23 & **0.48** \\  & SHFLC & 0.89 & **0.64** & 0.70 & 0.90 & **1.30** & **0.57** & 0.67 & **1.10** & 0.30 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Performance indices for various control cases under earthquakes without pulse-effect. Figure 12 illustrates the profiles of average inter-story drifts for uncontrolled, maximum passive control and SHFLC cases. In the figure, it can be seen that the SHFLC case is better than the maximum passive control in inter-story drift reductions of base-isolated structure. Compared with uncontrolled base-isolated structure, there is no obvious amplification in inter-story drifts in the SHFLC case. Furthermore, the inter-story drifts of the SHFLC case at the bottom of the superstructure have an appropriate reduction, which can be illustrated by the performance indices \(J_{4}\) shown in Tables 7 and 8, respectively.