# Effect of Nonlinear Hysteresis Details of Isolation System on In-Structure Response Spectra
## 1 Introduction
And it is difficult to control the initial stiffness in the case of the manufacturing process of lead rubber bearings (LRBs) because the initial stiffness varies depending on the quality of the lead core insertion. Because of this, there are no clear criteria for calculating the initial stiffness. However, it has been confirmed that its impact on the ISRS cannot be ignored [14], and it has become necessary to consider the initial stiffness, which has not been of interest until now. In addition, it may be difficult to determine conservatism for the ISRS because the peak for the effective period changes as the hysteresis behavior of an isolator varies depending on the isolator stiffness. In addition to stiffness, nonlinear hysteresis behavior can change due to seismic intensity, site property, and soil-structure interactions, and it is important to understand how the variability of hysteresis behavior due to these variables affects the ISRS. If we can consider the uncertainties of the variables affecting an ISRS and quantitatively reflect these uncertainties, we will be able to develop the criteria for designing the ISRS of isolated structures. Therefore, in this study, the variables that can affect nonlinear hysteresis behavior were selected, and the resulting ISRS variability was analyzed. The variables selected, which can affect nonlinear hysteresis behavior, were the initial stiffness of the isolator, the hysteresis models of isolators, and the seismic intensity. Secondary stiffness and characteristic strength are the most important properties in the design of isolators,and many studies on secondary stiffness and characteristic strength have been conducted, and design criteria have been presented [16,17]. For LRB, the secondary stiffness can be estimated by the shear modulus of the rubber and contributes to the calculation of the isolation frequency. If the target isolation frequency is determined, the secondary stiffness can be calculated, which can be an important parameter in the design. The characteristic strength can be estimated by the yield strength of the lead core and contributes to the energy dissipation capacity. That is, these parameters can be easily estimated by the material properties of the isolator, and the influence of these parameters on the ISRS were evaluated in many studies. Therefore, despite its importance for isolator design, these two variables were not considered in this study. In addition, because the actual behavior of the isolator is not an ideal bilinear model but rather behaves as a smooth curve at the yield point like the Bouc-Wen model, and a slight difference in the yield point can affect the ISRS, the sharpness of the yield point was selected as a variable. The effects on the ISRS shape by seismic intensity were also evaluated, because the maximum displacement of the hysteresis behavior, which can differ the effective period, varies depending on the seismic intensity. In summary, this study aims to suggest the consideration for the design ISRS of base isolated structures. The detailed goal is to identify the variables that affect the ISRS of an isolated structure and the resulting variability, and to provide a basis for determining peak frequency broadening and response amplitude for the development of a designed ISRS.