The response statistics of non-linear, second-order transformations to Gaussian loads

Abstract The paper describes the development of a method for statistical analysis of the response of a non-linear, second-order dynamic system subjected to a stationary, Gaussian forcing function. The method is particularly suitable for predicting extreme responses. The problem formulation expresses the response in terms of a second-order Volterra series, i.e., including a linear and a quadratic term. For this type of response process, the mean upcrossing frequency is found and asymptotic expressions are established that can be used to obtain closed form approximate solutions to the problems of extreme values or first passage of high levels.

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