# Effect of Nonlinear Hysteresis Details of Isolation System on In-Structure Response Spectra
## 5 Conclusions  
To evaluate the response of equipment installed in the seismically isolated structure and develop the ISRS for design, the influence of the variables, which can have a significant impact on the ISRS, was analyzed. Because the ISRS of isolated structures was significantly affected by the hysteresis behavior of the isolator, the initial stiffness of the isolator, seismic intensity, and hysteresis model were selected as variables that can affect the hysteresis behavior, and the analysis was performed. * Because of the seismically isolation system, the natural frequency corresponding to the deformation mode of the isolated superstructure becomes larger than the natural frequency of the fixed structure. Therefore, the peak of the spectral acceleration occurs at the shifted frequency. In addition, the response occurred larger at the stories far away from the middle story, which is the center of rotation of the structure. * The initial stiffness of the isolator significantly affected the shifted frequency, and the greater the initial stiffness, the greater the response. Conversely, as the initial stiffness decreased, the peak at the shifted frequency decreased, but as the isolation frequency decreased, the low-frequency response increased. High initial stiffness had a significant effect on the high-frequency response, including the natural frequency of the structure, while low initial stiffness had a significant effect on the low-frequency response, including the isolation frequency. * For high initial stiffness, as the seismic intensity increased, the maximum displacement and the low-frequency range, including isolation frequency, increased, and there was no significant change in the high frequency. In the case of small initial stiffness, response changes occurred only at the high-frequency range depending on the seismic intensity, but the variability was not large. Although the peak changed as the isolation frequency shifted according to the seismic intensity, it is expected to be included for the design seismic intensity. Figure 22: Comparison of 5F acceleration time history of isolated structure using bilinear and Bouc–Wen model according to initial stiffness (PGA = 0.2 g). * The difference between the bilinear model and the Bouc-Wen model affected the high-frequency range, including the structure frequency, and the smaller the initial stiffness, the more the response of the Bouc-Wen model decreased. Although the sharpness of the yield point does not affect the frequency variability, it is involved in the amplitude of the ISRS at the high-frequency range and had a large variability depending on the initial stiffness. If the design ISRS development requires consideration of the high-order mode response, the bilinear model would be appropriate. However, if not, it may be appropriate to evaluate it with the Bouc-Wen model. It was confirmed that variables that can affect the hysteresis behavior of the isolator affect the low- or high-frequency response of the ISRS. Criteria are needed that can include uncertainties, taking into account not only the response intensity but also the peak frequency shift. In this study, only variables that can affect the hysteresis behavior except for the secondary stiffness and the characteristic strength, such as the initial stiffness, the seismic intensity, and the hysteresis model, were selected to identify the variability of the ISRS. The initial stiffness of the isolator affected not only the high-frequency range but also the low-frequency range. In the low-frequency range, it is important to determine the peak broadening frequency by considering the frequency variability. In the high-frequency range, it is important to determine the ISRS intensity. In addition, the Bouc-Wen model was applied because it was expected that various isolation hysteresis behaviors could be expressed by adjusting the parameters of the Bouc-Wen model.