Journal
NONLINEAR DYNAMICS
Volume 45, Issue 1-2, Pages 95-108Publisher
SPRINGER
DOI: 10.1007/s11071-006-1461-3
Keywords
linear and nonlinear systems; Monte Carlo simulation; non-Gaussian excitations; nonlinear filter; random vibration; statistical linearization; stochastic differential equations
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The approach of nonlinear filter is applied to model non-Gaussian stochastic processes defined in an infinite space, a semi-infinite space or a bounded space with one-peak or multiple peaks in their spectral densities. Exact statistical moments of any order are obtained for responses of linear systems subjected to such non-Gaussian excitations. For nonlinear systems, an improved linearization procedure is proposed by using the exact statistical moments obtained for the responses of the equivalent linear systems, thus, avoiding the Gaussian assumption used in the conventional linearization. Numerical examples show that the proposed procedure has much higher accuracy than the conventional linearization in cases of strong system nonlinearity and/or high excitation non-Gaussianity.
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