Evaluation of the Modal Coupling Effect in Midstory Isolation Systems Based on Random Vibration Analysis

Xiao Song,Songtao Xue,Zeqi Lu

doi:10.1155/2021/9382235

Abstract

At present, the midstory isolation (MSI) technology has great potential for application in historical buildings’ retrofitting and multifunction buildings. The coupling effect due to the variability of the location of the isolation layer may amplify the structural seismic response and is required for in-depth analysis. This paper aims to evaluate the magnitude of the coupling effect and delimitate the region of the coupling effect to be considered. Based on the complex mode superposition method, the explicit formulas for calculating the random response of the simplified model are deduced. The root-mean-square (RMS) ratio of the shear force coefficient of the upper isolation system is adopted as the performance indicator to evaluate the coupling amplification effect of the MSI system. Parameter analysis indicates that the coupling region is closely related to the mass ratio and frequency ratio of the upper and lower structures to the isolation layer. In general, the region of the coupling effect to be considered can be divided into two parts according to parameters of frequency ratios, depending on the thresholds of the performance indicator. As the mass ratio of the upper isolation system to the entire system increases, one of the coupling regions shrinks and eventually disappears, indicating that the coupling amplification effect in this region can be neglected under certain conditions. Finally, the time-domain analysis of three representative numerical cases of MSI buildings was performed to verify the reliability of the results obtained from the frequency-domain analysis. The research results can provide technical guidance for the preliminary design of the MSI buildings.

Highlights

The midstory isolation (MSI) technology has great potential for application in historical buildings’ retrofitting and multifunction buildings. e coupling effect due to the variability of the location of the isolation layer may amplify the structural seismic response and is required for in-depth analysis. is paper aims to evaluate the magnitude of the coupling effect and delimitate the region of the coupling effect to be considered
Based on random vibration analysis, this study proposed a method to evaluate the coupling effect of the MSI systems
Explicit dynamic response formulas are derived for the MSI systems, the base isolation systems, and the fixedbase systems under white-noise excitation. e RMS ratio of the shear force coefficient of the upper isolation system is adopted as the performance indicator to evaluate the coupling amplification effect of the MSI system

Summary

Research Article

Evaluation of the Modal Coupling Effect in Midstory Isolation Systems Based on Random Vibration Analysis. Parameter analysis indicates that the coupling region is closely related to the mass ratio and frequency ratio of the upper and lower structures to the isolation layer. According to the above analysis, the relevant parameters of the structural dynamic equation (3) are the nondimensional parameters εls, εus, r1, and r2; the damping ratios ξls, ξiso, and ξus; and the frequency of upper isolation system ωiso. Substituting equations (16) and (17) in the resultant equations in Appendix, RMS of the absolute acceleration σ for the upper mass in the 3-DOF model can be obtained as an explicit function of the design parameters r1, r2, εls, εus, ξls, ξiso, and ξus. E results show that the seismic response of the upper isolation system can be reduced by slightly adjusting the frequency ratios εls and εus according to the characteristics of different regions. Frequency Response Analysis. e contours of the performance indicator Raui derived from the given mass ratios r1 and r2 and damping ratio ξiso, as well as the location of the

Peak line

Peak line B

Conclusion