Modelling and simulation of a wire rope based nonlinear vibration isolation system

A wire rope based vibration isolation system is a typical nonlinear passive vibration isolation system. Energy is transferred and dissipated through elastic deformation and inner friction. Based on a wire rope structure with both ends constrained, a nonlinear vibration isolation system with high-order stiffness and hysteretic damping was constructed. The Bouc-Wen model was adopted to characterize the hysteretic restoring force and a dynamic model was established for the system under harmonic displacement excitation. Expressions for equivalent stiffness and equivalent damping ratio were deducted. The equivalent stiffness includes linear, cubic and power function terms, and the system exhibits a softening-hardening characteristics. The equivalent damping ratio increases first and then decreases with vibration amplitude. The harmonic balance method based approximate analytical solution and the 4th-order Runge-Kutta method based numerical solution were adopted in numerical simulation. The results demonstrate that cubic stiffness has an effect on the resonant frequency varying characteristics and can eliminate the jump phenomena in a specific excitation amplitude range. The simulation results also reveal the influences of model parameters on system stiffness and damping. © 2020, Editorial Office of Journal of Vibration and Shock. All right reserved.