A New Solution Technique for Randomly Excited Hysteretic Structures

Keywords: Hysteretic Systems, Random Variations, White Noise Processes, and Response Approximation.

Abstract: An approximate procedure is developed for computing the probability density and statistical properties for the response of a hysteretic system under Gaussian white-noise excitations. In this procedure, the original system is replaced by another system belonging to the class of generalized stationary potential for which an exact solution is possible. The replacement is based on a criterion that the statistical average of the energy dissipation remains the same for substituting and substituted systems. The method is applicable to either bilinear or smooth type hysteresis and for either hardening or softening hysteretic behaviors without the restriction that the response be a narrow-band process or the energy dissipation be small. Comparison of computed results with available simulation results indicates that the proposed method is accurate for wide ranges of excitation levels and system parameters.