The Elliptic Harmonic Balance Method for the Performance Analysis of a Two-Stage Vibration Isolation System with Geometric Nonlinearity

This study develops a modified elliptic harmonic balance method (EHBM) and uses it to solve the force and displacement transmissibility of a two-stage geometrically nonlinear vibration isolation system. Geometric damping and stiffness nonlinearities are incorporated in both the upper and lower stages of the isolator. After using the relative displacement of the nonlinear isolator, we can numerically obtain the steady-state response using the first-order harmonic balance method (HBM1). The steady-state harmonic components of the stiffness and damping force are modified using the Jacobi elliptic functions. The developed EHBM can reduce the truncation error in the HBM1. Compared with the HBM1, the EHBM can improve the accuracy of the resonance regimes of the amplitude-frequency curve and transmissibility. The EHBM is simple and straightforward. It can maintain the same form as the balancing equations of the HBM1 but performs better than it.