Vibration statistics of the Duffing oscillator

Abstract

The stationary response of the Duffing oscillator excited by white noise is considered. Based on the associated Fokker-Planck equation, the joint moments, of all orders, of the displacement and velocity are obtained in closed-form, in terms of parabolic cylinder functions. An asymptotic expansion, valid for large values of a dimensionless parameter, is also presented. It is shown that all moments of the Duffing oscillator are bounded by the corresponding moments of the linear oscillator.