Random response of Duffing oscillator to periodic excitation with random disturbance

This paper discusses the random response of a non-linear Duffing oscillator subjected to a periodic excitation with random phase modulation. Effects of uncertainty in the periodic excitation and level of the system non-linearity on the response moments and non-Gaussian nature of the response caused by both the system non-linearity and the non-Gaussian loading are investigated. Results are presented in terms of the second- and the fourth-order moments as well as the excess factor of the response and some results are compared with those from the Monte Carlo simulation. An iterated linearisation technique is proposed to improve the accuracy of the numerical results for strongly non-linear systems.