Performance uncertainty estimation of a nonlinear vibration system

Abstract

In a mechanical system, parameter uncertainties always exist due to several reasons such as manufacturing tolerances, manufacturing process irregularity and environmental change. For instance, mass, stiffness, damping coefficient and friction coefficient which are design parameters of a vibration system may have uncertain characteristics caused by such reasons. Therefore, for a reliable design of a vibration system, the performance uncertainty which results from the system parameter uncertainties needs to be estimated accurately. In this paper, a performance measure is defined for a nonlinear vibration system and a statistical method to estimate the performance uncertainty using the first order reliability method (FORM) is employed. It was found that the FORM could provide good results even if the system of concern is nonlinear. Compared to the results obtained by Monte Carlo Simulation (MCS), the accuracy of the FORM applied to nonlinear system was verified.