## 3 Seismic Control Effectiveness of the TID for Base-Isolated Structures
### Displacement Response  
In this part, the displacement response of the isolated structure under ground motion excitation is used as the evaluation index of the control effectiveness of the TID. Specifically, the mean square and maximum values of the structural displacement are discussed below, respectively. Figure 11 presents the mean squared displacement responses for each storey of the three base-isolated structures, both with and without different mass ratio TIDs, subject to three various types of ground motion excitation. First of all, the TID has achieved visible control effectiveness under the three types of ground motion excitation, and the control effectiveness improved with the increase of the mass ratio. Comparing the isolated structures with different heights, the control effectiveness of the TID on low-rise isolated structures is obviously better than that on high-rise isolated structures. This is mainly due to the fact that the higher the structure, the greater the participation of high-order modes, and the more obvious the limitations of single-mode control. Alternatively, the control effectiveness of the TID on different types of ground motion excitation has obvious discreteness, and this discreteness is also affected by the altitude of the base-isolated structure. For example, the control effectiveness of the TID on the 15-story isolated structure under the near-fault ground motions without pulse subset is significantly smaller than that in other cases. Another consideration is the peak displacement of the base-isolated structure. Figure 12 displays the peak displacement responses of the structure, comparing cases with and without the TID. By comparing the control effect of TID on peak displacement, it can be observed that TID has a less significant influence on peak displacement than on mean square displacement, particularly for the 15-storey structure. This is mainly due to the fact that the TID, like traditional passive TMD, cannot effectively play a controlling role in the initial stage. Therefore, if the structure reaches the peak displacement at the initial stage of ground motion excitation, the TID cannot fully exert the control effect at this time, which results in poor reduction for the peak displacement. In some cases, increasing the mass ratio of TID can offset the disadvantages of its control delay, with this effect being more pronounced on lower stories. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Ground Motions Type**} & \multicolumn{3}{c}{**Far-Fault**} & \multicolumn{3}{c}{**Near-Fault (No Pulse)**} & \multicolumn{3}{c}{**Near-Fault (Pulse)**} \\ \hline
**Structure** & **Parameter** & \(m_{d}\) **(ton)** & \(f^{opt}\) & \(\xi_{d}^{opt}\) & \(m_{d}\) **(ton)** & \(f^{opt}\) & \(\xi_{d}^{opt}\) & \(m_{d}\) **(ton)** & \(f^{opt}\) & \(\xi_{d}^{opt}\) \\ \hline \multirow{3}{*}{\(5\)-Storey} & \(\mu=0.05\) & 2.067 & 0.964 & 0.111 & 2.067 & 0.962 & 0.110 & 2.067 & 0.957 & 0.109 \\  & \(\mu=0.1\) & 4.135 & 0.933 & 0.154 & 4.135 & 0.930 & 0.152 & 4.135 & 0.922 & 0.150 \\  & \(\mu=0.2\) & 8.269 & 0.878 & 0.212 & 8.269 & 0.875 & 0.207 & 8.269 & 0.864 & 0.204 \\  & \(\mu=0.05\) & 232.535 & 0.963 & 0.111 & 232.535 & 0.966 & 0.110 & 232.535 & 0.961 & 0.110 \\ \multirow{3}{*}{\(10\)-Storey} & \(\mu=0.1\) & 465.071 & 0.931 & 0.155 & 465.071 & 0.935 & 0.154 & 465.071 & 0.928 & 0.152 \\  & \(\mu=0.2\) & 930.141 & 0.876 & 0.213 & 930.141 & 0.883 & 0.211 & 930.141 & 0.873 & 0.208 \\ \multirow{3}{*}{\(15\)-Storey} & \(\mu=0.05\) & 1025.385 & 0.975 & 0.111 & 1025.385 & 0.999 & 0.114 & 1025.385 & 0.973 & 0.111 \\  & \(\mu=0.1\) & 2050.770 & 0.948 & 0.155 & 2050.770 & 0.980 & 0.160 & 2050.770 & 0.945 & 0.155 \\ \multirow{3}{*}{\(15\)-Storey} & \(\mu=0.2\) & 4101.539 & 0.900 & 0.214 & 4101.539 & 0.945 & 0.223 & 4101.539 & 0.897 & 0.213 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Optimum parameters of the TID with different mass ratios for the three base-isolated structures.