Response of an oscillator with non-linear damping and a softening spring to non-white random excitation

Abstract

A generalised method of stochastic averaging is applied to a class of non-linear oscillators which have linear-plus-quadratic damping and linear-plus-cubic stiffness, with a softening spring characteristic. It is shown that, by approximating the total energy envelope of the oscillator as a one-dimensional Markov process, expressions for various response statistics can be deduced. A simple modification to the method is proposed which takes further account of the shape of the input spectrum. Comparisons between simulation results and predictions from the proposed theory indicate that the modification to the theory leads to improved accuracy. Comparisons between theory and simulation for the mean first passage time reveal that this statistic is sensitive to the magnitude of the input spectral bandwidth. The application of the theory to the prediction of the roll response of ships and transport barges to irregular wave excitation is discussed briefly.