Stochastic analysis of oscillators with non-linear damping

The response of a class of oscillators with non-linear damping to stochastic excitation is considered. A partial differential equation which describes approximately the probability density function of the response amplitude is derived. The stationary and non-stationary solutions of this equation are examined. The soundness of the method is tested by comparing the solutions generated by its application to problems with known solutions. The Van der Pol and Rayleigh oscillators are included in the example problems studied.