Performance analysis of a geometrically nonlinear isolation system subjected to high levels of excitation

This study develops a modified harmonic balance method (HBM) and uses it to analyze the vibration isolation performance of a geometrically nonlinear isolation system subjected to high levels of excitation. The modified 5th-order Taylor series expansion (TSE) is applied to simplify the geometrically nonlinear stiffness (GNS) and geometrically nonlinear damping (GND). Using a modified elliptic harmonic balance method (EHBM), we can calculate the approximate free vibration frequencies consistent with the exact solutions. After illustrating the limitation of the high-order solution assumed by Jacobi elliptic functions, a modified HBM is proposed to solve the damped cubic-quintic Duffing (CQD) equation with high-level external excitation. The stability analysis is obtained, and the characteristics of unstable regions are shown according to different values of the damping coefficient. The results show that GNS and GND profoundly affect the high-order harmonic components of amplitude-frequency response and force transmissibility. The characteristics of low frequency and resonance regimes with or without quasi-zero stiffness (QZS) are different as the amplitude of excitation increases. The modified TSE and HBM are desirable and straightforward for the detailed study of the characteristics of the GNS and GND vibration isolation system.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

This study develops a modified harmonic balance method (HBM) and applies it to analyze the vibration isolation performance of a geometrically nonlinear isolation system under high levels of excitation. The results show that the geometrically nonlinear stiffness (GNS) and geometrically nonlinear damping (GND) significantly affect the high-order harmonic components of the amplitude-frequency response and force transmissibility.