A non-Gaussian closure approach is applied to random response of a hysteretic structure subjected to Gaussian white noise excitation. The non-stationary response mean squares and stationary power spectral densities of the displacement, velocity and hysteretic component of the restoring force are predicted. In addition, due to their importance in characterizing hysteretic structures, the mean value and root-mean-square (RMS) of energy dissipation rate which are the second and fourth-order response statistics, respectively, are also computed. It is shown that the mean value of the stationary energy dissipation rate depends only on the amplitude of external excitation. Various structural parameters which determine different elastoplastic behaviours of the response are considered in the study. The convergence of the method is demonstrated by increasing the number of high-order moments in the analysis. Favourable comparisons with numerical simulation and other techniques are observed. This approach has the advantage of numerically generating equations of high-order moments which are used in estimating non-Gaussian responses. The non-Gaussian random response of complex nonlinear behaviour of structures such as hysteresis can be estimated satisfactorily.

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Journal Transactions of the Canadian Society for Mechanical Engineering
Liu, Q., & Afagh, F. (1994). Random response and energy dissipation of a hysteretic structure subjected to white noise excitation. Transactions of the Canadian Society for Mechanical Engineering, 18(4), 333–352.