Rocking Effect of Three-Dimensional Base Isolation Systems with Large Height–Width Ratios

Three-dimensional base isolation systems (3D-BISs) are rarely applied to multistory and high-rise buildings due to the rocking effect, and limited research on the coupled translation-rocking motion mode has hindered the development of 3D-BISs with large height–width ratios. In this study, a simplified analysis model is proposed for the 3D-BIS, and then the modal analysis is carried out to reveal the influence of eccentricity ratios and height–width ratios on the dimensionless frequency ratios of the system. Moreover, with varying damping ratios and rocking stiffness, particular attention is dedicated to the vibration transmissibility characteristics of a 3D-BIS with a height–width ratio above 4 and a mass of 40 tons. The results show that a greater eccentricity ratio or height–width ratio will increase the coupled response of the superstructure, while an increase in the damping ratio can reduce the rocking effect of the 3D-BIS. Providing additional rocking stiffness is beneficial to decoupling the translation from the rocking motion but may increase the acceleration response of the superstructure, so proper rocking stiffness should be set for the 3D-BIS to balance these effects. The analysis results of this study lay a foundation for the optimization design of 3D isolators and 3D-BISs.