Analysis of the Effects of Nonlinear Damping on A Multiple-Degree-of-Freedom Quasi-Zero-Stiffness Vibration Isolator

Abstract

Designing and analyzing performance of vibration isolators is important for many engineering industries. An active area of current research is the design and improvement of vibration isolators that exhibit the Quasi-Zero-Stiffness (QZS) property. QZS vibration isolators have a high static and low dynamic stiffness, allowing them to support a large load while effectively isolating vibrations over a range of frequencies. Vibration isolation in multiple directions or modes of motion (degrees of freedom) is also important for many practical engineering applications. The intent of the present research is to assess the effect of nonlinear damping on a multi-directional, QZS vibration isolator. A two degree-of-freedom vibration isolator was 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 geometric relationships led to nonlinear expressions for damping. 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 model for both degrees of freedom. Absolute transmissibility was used to compare the performance of the system with linear damping 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 features are attributed to the nonlinearities in the vibration isolation system. 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.