# Effect of Nonlinear Hysteresis Details of Isolation System on In-Structure Response Spectra
## 4 ISRS According to the Initial Stiffness of Isolator  
To demonstrate that the isolation system applied properly, a graph comparing the base shear forces of the fixed and isolated structure is shown in Figure 10. The seismic isolation effect seems to be well demonstrated, as the base shear force of the isolated structure is significantly reduced by up to 60% compared to the fixed structure. Figure 11 is a graph showing the average ISRS obtained from the analysis using 10 sets of input motions with a PGA of 0.2 g on an isolated structure with a stiffness ratio of 0.01 applied. In this Figure, the ISRS of the fixed structure was compared by story. In the case of fixed structures, the boundary conditions are fixed at the 0 story, and because it is the point where motions are input, it shows the same as the response spectrum of the input motions. And as the story goes up, the peak at 8 Hz, the natural frequency of the structure, is amplified, showing a typical amplification by structural vibration. In the case of the isolated structure, the ISRS was reduced overall compared to the fixed structure due to the isolation effect. However, at 0F and 1F, a response greater than that of the fixed structure occurred at the shifted frequency of the structure (approximately 13 Hz). That is, the response of the structure was significantly reduced due to the isolation effect, but there were also ranges where the effect was less applied. In addition, unlike the ISRS of the fixed structure, the ISRS of the isolated structure is not amplified as the story becomes higher, but the peak at the shifted frequency of the structure (approximately 13 Hz) is amplified as the height difference from 3F, the center of rotation, increases. As can be seen in the Figure, the ISRS of the isolated structure was the least at 3F and the largest at 0F and 5F, which are farthest from the 3F. In the case of 0F and 1F, the response was even larger than that of the fixed-base structure. Around the isolation frequency of 0.5 Hz, a peak did not occur. This is because, as can be seen in the hysteresis behavior of the isolator shown in Figure 12, the seismic intensity does not reach the target displacement and behaves within a small displacement. It is judged that this caused the behavior to occur in a small cycle range and that the response occurred in a frequency range slightly greater than 0.5 Hz (about 0.8 to 1.1 Hz) as the effective stiffness increased. Figure 10: Base shear force of fixed and isolated structures. Figure 9: Time history of input motions matching with Reg. Guide 1.60 design response spectrum. Figure 13 shows the ISRS for each story according to the initial stiffness with different stiffness ratios. As the initial stiffness changes, the ISRS response difference at the shifted structure frequency occurs the most, and it can be confirmed that it generally affects the high-frequency range. Looking at the hysteresis behavior of the isolator by the stiffness ratio in Figure 14, the smaller the stiffness ratio (larger the initial stiffness), the greater the tendency for the maximum displacement to decrease. This means that as the stiffness increases, a strong force is applied to cause the initial displacement, so the maximum displacement decreases, and the high-frequency response increases as the superstructure behaves as a rigid body with the isolator. Conversely, as the initial stiffness decreases, the effective stiffness decreases, and the response at a low frequency increases. Figure 15 shows the amplification ratio compared to the fixed response for the low-frequency range (0.5 to 1.5 Hz), where the isolation frequency changes depending on the stiffness ratio, and the high-frequency range (10-20 Hz), where the frequency of the structural mode varies. The maximum ratio of the fixed and isolated ISRS in the low and high-frequency ranges was shown for each story in Figure 15. As the initial stiffness was smaller (the  
Figure 11: ISRS of fixed and isolated structures by story (PGA = 0.2 g, \(k_{d}/k_{u}=0.01\)).