Moment Analysis of a Duffing Oscillator Subjected to Non-Gaussian Random Excitation by Using the Equivalent Non-Gaussian Excitation Method and the Equivalent Linearization

An approximate analytical method is proposed to estimate the statistical moments up to the 4th order of the response of a Duffing oscillator subjected to non-Gaussian random excitation. The non-Gaussian excitation is prescribed by a wide class of probability densities and the power spectrum with bandwidth parameter. The moment equations for the system response are derived from the equation of motion of the system and the stochastic differential equation governing the excitation. However, they are not closed due to the complexity of the diffusion coefficient of the stochastic differential equation for the excitation and the system nonlinearity. Therefore, applying the equivalent non-Gaussian excitation method and the equivalent linearization, a closed set of the moment equations are obtained approximately. In numerical examples, we analyze a Duffing oscillator under non-Gaussian excitation with various shapes of probability densities. the response moments obtained by the present method are compared with Monte Carlo simulation results.