# Effect of Nonlinear Hysteresis Details of Isolation System on In-Structure Response Spectra
## 3 Analysis Model and Input Ground Motions
In general, the axial stiffness of the isolator is large enough to support the superstructure. However, the change in the horizontal stiffness due to a change in the axial force may affect the hysteresis behavior, and the variability of the axial force can also be an uncertainty parameter. In the case of an isolator such as friction pendulum bearings, the axial force can have a significant effect because the horizontal friction force caused by the normal force applied to the pendulum contributes to the restoring force. However, in the case of the LRB assumed in this study, variability in the axial force does not cause a significant variation in the horizontal stiffness unless buckling occurs, but that may affect the energy dissipation. Because this study aimed at parameters that can affect the shape of the hysteresis behavior, the effect of energy dissipation was not considered. This is because energy dissipation is a secondary factor resulting from the deformed hysteresis behavior. Therefore, in this study, the variability of the initial stiffness was considered first, without considering the variability of the axial force. If other isolator models, such as friction pendulum bearings, are applied, it will also be necessary to consider the variability of the axial force. \begin{table}
\begin{tabular}{c c} \hline
**Properties** & **Values** \\ \hline Weight (kN) & 637.7 \\ \(W\) & 38.26 \\ \hline Characteristic strength (kN) & 38.26 \\ \(Q_{d}/W\) & 0.06 \\ \hline Target frequency (Hz) & 0.5 \\ \(f_{isol}\) & 641.5 \\ \hline Stiffness ratio & 0.01 & 0.05 & 0.08 \\ \(k_{d}/k_{u}\) & 64,152.4 & 12,830.5 \\ \hline Initial stiffness (kN/m) & 64,152.4 & 12,830.5 & 8019.1 \\ \(k_{u}\) & 641.52 & 5346.0 \\ \hline \end{tabular}
\end{table} 
Table 1: Properties of isolator. Figure 6: Lumped mass stick model and mode shape. In addition, for a comparison between the bilinear and Bouc-Wen models, the exponent that determines the sharpness of the yield point was modeled with a different exponent (Table 1, Figure 7). The results of the modal analysis of the fixed and isolated structures are presented in Figure 6, and as expected, the second mode frequency of the isolated structure was found to be slightly larger than the first mode frequency of the fixed structure. The input motions were used by generating artificial ground motions that match to the design response spectrum with a PGA of 0.2 g and a damping ratio of 5% specified in Reg. Guide 1.60 using a stochastic method [38; 39]. The seismic intensity of 0.2 g was determined to be the level at which NPPs can operate normally even if an earthquake occurs (Operating Basis Earthquake, OBE). To ignore the variation that may occur due to the ground motion time history matching with the target spectrum, 10 sets were generated, and the results were averaged by these input ground motions. The response spectra of the generated ground motion time histories and the target response spectrum are depicted in Figure 8, and the time history of the input motions is depicted in Figure 9. In addition, these input motions were scaled with PGAs of 0.3 g, 0.4 g, and 0.5 g for the analysis of increased seismic intensity. Figure 8: Response spectra of input motions. Figure 7: Parameters for the Bouc–Wen plasticity property [33].