Analysis of the effects of nonlinear damping on a multiple-degree-of-freedom quasi-zero-stiffness vibration isolator

Abstract

In the present paper the effect of nonlinear damping on a multi-directional, Quasi-Zero-Stiffness (QZS) vibration isolator is assessed. A two degree-of-freedom vibration isolator is considered, the design consisting of an X arrangement of two struts comprising concentric magnets known to exhibit quasi-zero-stiffness. Nonlinear damping was accounted for in the system through rotational friction at the joints and damping in line with the struts themselves. The equations of motion were derived for each degree of freedom separately, namely transverse and twist motions, using the Energy method and Lagrange-Euler equations. The equations of motion were solved analytically using the Harmonic Balance method and numerically via Simulink. The numerical results validated the analytical predictions for both degrees of freedom. Absolute transmissibility was used to compare the performance of the system with both linear and nonlinear damping. Damping coefficients were found for optimal performance in each degree of freedom of the isolator. The transmissibility curves were optimised with no linear damping, and low strut and rotational damping coefficients. Complex attributes of the response were identified and discussed including a shift in the time averaged response and non-periodic motion in the response under certain conditions. These complexities can be reduced through a careful selection of linear and nonlinear damping coefficients. The research supports the hypothesis that nonlinear damping can improve the performance of quasi-zero-stiffness vibration isolators and identifies complex behaviours that must be considered in the isolator design.