Response of Linear Systems to Quadratic Gaussian Excitations

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Abstract
Probability density functions, mean crossing rates, and other descriptors are developed for the response of linear systems to squares of Gaussian excitations. The analysis is based on discrete approximations of the spectrum of the Gaussian excitation. Accordingly, the response can be expressed as a finite quadratic form in Gaussian variables, whose characteristic function has a closed form. The characteristic function can be inverted by Fast Fourier Transform algorithms to find the first order probability of the response. Several approximations are applied to determine crossing and peak characteristics of the response. The proposed methodology is applied to estimate structural response to wind loads and the mean failure rate of systems subjected to bivariate Gaussian stress processes.

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