An approximate method for solving force and displacement transmissibility of a geometrically nonlinear isolation system

Abstract

This study presents a modified harmonic balance method, which is used to solve the force and displacement transmissibilities of a vibration isolator with both the quasi-zero-stiffness and geometrically nonlinear damping. The steady-state response of the nonlinear isolation system is obtained by Jacobi elliptic functions, and is used to modify the harmonic components of stiffness and damping force in the harmonic balance method, which can reduce the truncation error produced by the trigonometric Fourier series. When the modified harmonic components are combined based on the orthogonality condition, the elliptic harmonic balance method (EHBM) is obtained. The results show that the amplitude–frequency response curve, and force and displacement transmissibilities obtained by using the EHBM can be compared well with those obtained by using the fourth order Runge–Kutta method. The EHBM can be used to improve the accuracy of the results at the resonance and high frequency regimes. The EHBM is simple and straightforward for the detailed study of the vibration isolation characteristics of the geometrically nonlinear isolator.