Consideration of Non-Gaussian Hysteretic Response Properties of MDOF-Systems by Use of Equivalent Linearization

by H. J. Pradlwarter, Univ of Innsbruck, Austria,

Document Type: Proceeding Paper

Part of: Structural Safety and Reliability


The stationary stochastic response of nonlinear MDOF-systems is analysed by equivalent linearization (EQL). Non-Gaussian properties of the state vector y are taken into account by utilizing nonlinear transformations y(x) between the nonlinear state vector y and its linearized (Gaussian) state vector x. The consideration of non-Gaussian properties significantly improves the estimates for the first two moments and makes EQL suitable for strongly nonlinear systems where the joint distribution deviates considerable from a jointly normal. The non-Gaussian joint distributions of y is represented by its marginal distributions and by modified correlation coefficients applicable for Gaussian distribution. The approximate shape of all marginal distribution is found by Monte Carlo simulation of non-Gaussian initial state vectors y and numerical integration over a short time interval. Finally, the procedure is applied to a six storey frame structure condensed to a six degree of freedom system. The colored excitation is modelled by filtered white noise.

Subject Headings: Gaussian process | Stochastic processes | Stationary processes | Vector analysis | Linear analysis | Nonlinear response | Monte Carlo method

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