Generalization of the equivalent linearization method for non-linear random vibration problems

The method of equivalent linearization is generalized such that the response of a non-linear oscillator subject to both parametric and external random white-noise excitations can be determined approximately. The main objective of the new method is to obtain a closed system of differential equations for certain statistical moments of the response. This can be achieved by linearizing the drift term of the corresponding Itô-equations and by replacing the square of the diffusion term by a second degree polynomial. It is found that the accuracy of the mean square amplitudes is improved considerably compared with the original equivalent linearization.