# Effect of Nonlinear Hysteresis Details of Isolation System on In-Structure Response Spectra
## 1 Introduction  
In important facilities, such as nuclear power plants, plant facilities, or data centers, the safety of not only the structure but also the equipment and devices installed in the structure is very important. If major equipment are damaged and cannot perform their functions, it can lead to secondary damage; in the case of NPPs, core damage can cause more serious social damage. To reduce the response of all equipment in the structure, it would be more efficient to design the entire structure as a seismically isolated system. By allowing the structural system to behave as a long period structure, not only will the base shear force of the structure be greatly reduced, but the acceleration seismic response on all floors can also be reduced. Therefore, the floor response spectra (FRS) or in-structure response spectra (ISRS), which are used to evaluate the safety of equipment installed in the structure, would also be greatly reduced due to the isolation system. The evaluation of ISRS is an important procedure in evaluating the safety of not only NPPs but also other structures, and the ISRS criteria for NPPs are presented as relatively more specific and detailed [1; 2]. Nevertheless, the ISRS criteria for isolated structures have not been established, and it is not clear whether the ISRS criteria for fixed structures should be applied. This is because, in the ISRS of isolated structures, the variables of isolator characteristics dominate the variables of mechanical properties of the structures, site response characteristics, and input ground motions. In order to identify the problems and develop the ISRS for isolated structures, several studies on the equipment in an isolated structure have been conducted [3; 4; 5; 6; 7; 8]. Although the isolation system could significantly reduce the floor response, it had a disadvantage where the displacement of the isolator increased further as the acceleration response decreased. In addition, it was confirmed that there were cases where the response was large during periods other than the targeted isolation period, and that this was greatly affected by the stiffness of the isolator. A study has also been conducted to experimentally evaluate the nonlinear response of isolated structures [9]. Experimental verification was performed due to the difficulty in evaluating the nonlinear characteristics and high-frequency response of the isolator and the limitations of existing numerical analyses. As a result, it was confirmed that the nonlinear response characteristics of the isolator have a significant impact on the seismic response of the structure. Therefore, it became important to identify the influence of the mechanical properties that determine the nonlinear characteristics. An isolator generally behaves bilinearly, and their behavior is determined by the main mechanical properties such as initial stiffness (pre-yield stiffness), secondary stiffness (post-yield stiffness), and characteristic strength. Once the isolation period has been determined, the mechanical characteristics of the isolator can be determined accordingly, and these characteristics have been verified through various experimental and analytical studies. Many studies have been conducted to analyze the influence of these mechanical characteristics of an isolator on the ISRS [10; 11; 12; 13; 14; 15]. The initial stiffness of an isolator is generally expressed as a ratio of secondary stiffness, and because it is relatively difficult to calculate [16] compared to the other characteristics of an isolator and is not considered to be very important, few studies have been conducted on initial stiffness. Secondary stiffness controls the frequency of the isolated structure, and the characteristic strength controls the damping. The initial stiffness of the seismic isolator does not have a significant effect on the seismic isolation effect of the isolated structure itself.