Approximate probability distributions of certain response variables are obtained for hysteretic systems under Gaussian white-noise excitations. The approximate method used is a generalization of a dissipation-energy-balancing procedure, developed previously for nonlinear but basically nonhysteretic systems. Some new issues related particularly to hysteresis models are explained and resolved. The method is applicable to either bilinear or smooth-type hysteresis 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.

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