# Effect of Nonlinear Hysteresis Details of Isolation System on In-Structure Response Spectra
## 4 ISRS According to the Initial Stiffness of Isolator
### ISRS According to Sharpness of Yield Point  
All the preceding results were the ISRS with an isolator of a bilinear hysteresis model. Because the realistic hysteresis behavior has a smooth curve at the yield point like the Bouc-Wen model, the effects on the ISRS by the sharpness of the yield point were examined. Figure 19 is the ISRS in which a 0.2 g input motion was input to an isolated structure with the same stiffness ratio of 0.01 and different sharpness of the yield point. In the case of  
Figure 17: Hysteresis behavior according to seismic intensity (\(k_{d}/k_{u}=0.01\)).  
Figure 18: ISRS of isolated structure according to seismic intensity and initial stiffness.  
high initial stiffness, there was a slight difference at high frequencies that were greater than the structural frequency, but it did not have a significant effect overall. Looking at the hysteresis behavior corresponding to the stiffness ratio of 0.01 in Figure 20, there was almost no difference between the two models, but the smaller the initial stiffness, the more apparent the difference. In the bilinear model, the stiffness before and after yielding changes rapidly, whereas in the Bouc-Wen model, the stiffness changes gradually and forms a smooth curve. Therefore, the smaller the initial stiffness, the larger the difference in the sharpness of yield point is thought to be. This difference affects the second (approximately 13 Hz) and third mode (approximately 33 Hz) frequencies of the isolated structure, which are the first and second structural mode frequencies, respectively, in the ISRS (Figure 21). When the initial stiffness was very large, the response of the bilinear model occurred larger in the modal frequency except for the isolation frequency. The Bouc-Wen model showed a peak only at the second mode frequency of the isolated structure and did not show a large response at higher modal frequencies. As the initial stiffness decreased, the response at higher modal frequencies decreased in both models, but the response of the Bouc-Wen model decreased more significantly. Because the stiffness of the Bouc-Wen model gradually changes, it appears that the response decreases at the structural frequency. That is, it was confirmed that the sharpness of the yield point was related to the initial stiffness of the isolator and had a significant influence on the high-frequency range. Figure 22 is a graph comparing the acceleration time history on the 5F according to the hysteresis model for stiffness ratios of 0.01 and 0.12. The acceleration response of the Bouc-Wen model was small overall, and the 2.5 to 3.5 s range was zoomed and displayed next to the time history graph to see the response in the high-frequency range. It was confirmed that the response of the Bouc-Wen model decreased in the range with many high frequency contents and the cycle lengthened. Therefore, if the design ISRS is designed to be based on the ideal bilinear model, there can be an overestimation in the high-frequency range. 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.  
Figure 19: Comparison of ISRS using bilinear and Bouc–Wen model (PGA = 0.2 g, \(k_{d}/k_{u}=0.01\)).  
Figure 21: Comparison of ISRS using bilinear and Bouc–Wen model according to initial stiffness (PGA = 0.2 g, 0F).  
Figure 20: Comparison of hysteresis behavior using bilinear and Bouc–Wen model according to initial stiffness (PGA = 0.2 g).