Quasi-harmonic analysis of the behaviour of a hardening Duffing oscillator subjected to filtered white noise

Abstract

The behaviour of a hardening Duffing oscillator subjected to narrow band random excitation is examined. The influence of possible jumps, between competing states, on the probability distribution of the response amplitude is addressed. A quasi-harmonic approximation of system behaviour is adopted which is capable of reproducing the observed concave shape of probability functions and compares well with predictions obtained via stochastic averaging techniques and with digital simulations.