Effect of damping nonlinearity on the dynamics and performance of a quasi-zero-stiffness vibration isolator

Quasi-zero-stiffness (QZS) vibration isolators that take advantage of stiffness nonlinearity are commonly studied with linear damping elements. This paper concerns the effects of damping nonlinearity on their dynamics and performance. Geometric nonlinear damping originating from horizontal and rotational dampers is considered. Analytical expressions for displacement and force transmissibility and stability of the isolator are derived using the harmonic balance method and, especially for large-amplitude excitation, numerical continuation. The beneficial effect of nonlinear damping on the removal or minimization of unwanted isolated subharmonic branches is shown. Metrics are defined to assess the performance of the QZS isolator. Results indicate that, for both small and large-amplitude base excitation, increasing nonlinear damping can effectively suppress peak transmissibility; however, as base excitation level increases, larger nonlinear damping increases transmissibility at intermediate to high frequencies. On the other hand, results reveal that for all levels of force excitation, force transmissibility at higher frequencies is not dependent on the variations of nonlinear damping and is just a function of the linear damping. Whatever the input level, the peak transmissibility of the forced QZS isolator can be reduced by increasing nonlinear damping.