Analytical and Numerical Investigation of Quasi-Zero Stiffness Vertical Isolation System

Abstract

A novel nonlinear isolation system designed for buildings is proposed to isolate vibrations in the vertical direction. The system is characterized by quasi-zero stiffness (QZS) obtained by combining linear springs in parallel with disk springs having nonlinear stiffness, including a region with negative stiffness. Static analysis was first applied to establish the force-displacement relation of the bearings and then determine the dynamic equations of motion. Two approximate analytical methods, the average method (AM) and harmonic balance method (HBM), were applied to solve this nonlinear vibration problem, and their suitability was examined. Based on the theoretical response, the transmissibility function was defined to gain insight into the system’s dynamic characteristics and evaluate the isolation properties. The resulting curves show that the QZS system can be effective for vertical isolation, with results dependent on external input magnitude and the damping level. Larger-amplitude excitation and higher damping level tend to increase the isolation starting frequency above which the transmissibility reduces the vibration of the superstructure. Finally, the nonlinear transmissibility curves were compared with equivalent linear curves, and a numerical comparison between a traditional building and a QZS vertically isolated building under seismic excitations was conducted. The comparison revealed significant advantages to adopting the QZS system in vertical isolation.