## 2 Methodology
### Excitation Data  
The fixed base, passively isolated, and MRE controlled isolated structures are subjected to earthquake excitations in form of acceleration for analyzing their responses. In the current study, near-fault earthquake ground motion [1, 8, 11, 12, 13, 63, 64, 65, 66, 67, 68, 69, 70, 71] time histories have been selected from 1999 Chi-Chi, 1979 Imperial Valley, and 1999 Kocaeli earthquakes. These records are taken from Taichung, Brawley Airport, and Izmit stations, respectively [72]. Furthermore, another set of earthquake time histories, which are recorded from the same earthquake events under the same site conditions with the fault located at a distance far away from the site, is selected to demonstrate far-field ground motion characteristics [1, 8, 11, 12, 13, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73]. The properties and description of the adopted time histories for near-fault and far-fault earthquakes are presented in Tables 4 and 5, respectively. The ground motion time histories are adapted from the PEER Strong Motion Database [72]. We aimed to acquire two sets of time history records (i.e., near-fault and far-fault) with the same peak ground acceleration of each earthquake (Chi-Chi 1999, Imperial Valley 1979, and Kocaeli 1999) for a more accurate and fair comparison of the results [69]. Thus, the selection of records has been made with more diligence. If the ground motion time histories of each earthquake were selected randomly (different peak acceleration values and/or site conditions), the meaningful comparison of the responses could not have been established with confidence. Thus, we aimed to eliminate this contradiction by selected ground motion records with the same peak acceleration values under the same site conditions [69, 72]. The acceleration and velocity records of the adopted earthquake time histories are shown in Figures 3-5. The same vertical scale in the plots has been adopted for near-fault and far-fault records for a particular earthquake loading to demonstrate the difference between the earthquakes. These figures show the significant velocity pulses for the near-fault ground motions compared to far-field records [70] despite having the same peak ground acceleration, which is one of the main characteristics of destructive near-field earthquake records [1, 8, 11, 12, 13, 63, 64, 65, 67, 68, 69, 70, 71, 73]. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Event** & \(\mathbf{M_{w}}\) & **Station** & **PGA** & **PGV (cm/s)** & **Distance to a Fault (km)** \\ \hline Chi-Chi (1999) & 7.6 & Taichung & 0.2 g & 36.3 & 9.5 \\ Imperial Valley (1979) & 6.9 & Brawley Airport & 0.16 g & 36.6 & 8.5 \\ Kocaeli (1999) & 7.8 & Izmit & 0.17 g & 22.6 & 4.8 \\ \hline \end{tabular}
\end{table} 
Table 4: Near-fault earthquake time histories. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Event** & \(\mathbf{M_{w}}\) & **Station** & **PGA** & **PGV (cm/s)** & **Distance to a Fault (km)** \\ \hline Chi-Chi (1999) & 7.6 & Ilan & 0.2g & 11.8 & 49 \\ Imperial Valley (1979) & 6.9 & Compuertas & 0.15g & 9.5 & 35 \\ Kocaeli (1999) & 7.8 & Fatih & 0.16g & 12 & 64.5 \\ \hline \end{tabular}
\end{table} 
Table 5: Far-fault earthquake time histories. In this way, a total of 12 simulations have been performed for each of the fixed base, passively isolated, and MR elastomer-based isolated structures using MATLAB. The cumulative number of simulations for all the three structures and 12 load cases totals 36. A total of 306 responses were compiled and analyzed, after which the results were processed, compared, presented, and discussed. Figure 4: Near-fault and far-fault ground motions recorded at the Imperial Valley earthquake in 1979. (**a**) Acceleration time histories for near-fault and far-fault earthquake records. (**b**) Velocity time-histories for near-fault and far-fault earthquake records [72]. Figure 3: Near-fault and far-fault ground motions recorded at the Chi-Chi earthquake in 1999. (**a**) Acceleration time histories for near-fault and far-fault earthquake records.