Analytical study of quasi-zero stiffness vibration isolator with uncertain parameters based on arbitrary polynomial chaos expansions method

Quasi-zero stiffness (QZS) vibration isolators have broad application prospects in effectively suppressing low-frequency vibrations; most current quasi-zero stiffness vibration isolator response studies are based on the ideal case of design parameters. Considering the structural complexity of quasi-zero stiffness vibration isolators, the existence of parameter errors is difficult to ignore. Due to the strong nonlinearity of the QZS system, small changes in the system parameters may lead to a sharp deterioration of the vibration isolation performance in an undesired direction. In this paper, the classical QZS system response under the influence of parameter uncertainties is investigated by using the arbitrary polynomial chaos expansions method (aPCE), and the effects of the individual and coupling effects of the uncertainties of the main parameters on the steady-state displacement response of the system are analyzed. On this basis, the distribution law of the steady-state response under non-normal parameter distributions is further investigated, and Sobol global sensitivity indices in different frequency bands under the coupling effect are studied.