Extension of an Itô-based general approximation technique for random vibration of a BBW general hysteris model part II: Non-Gaussian analysis

Abstract

The work presented in this paper constitutes the second phase of on-going research aimed at developing mathematical models for representing general hysteretic behavior of structures and approximation techniques for the computation and analysis of the response of hysteretic systems to random excitations. In this second part, the technique previously developed by the authors for the Gaussian response analysis of non-linear systems with general hysteretic behavior is extended for the non-Gaussian analysis of these systems. This approximation technique is based on the approach proposed independently by Ibrahim and Wu-Lin. In this work up to fourth order moments of the response co-ordinates are obtained for the Bouc-Baber-Wen smooth hysteresis model. These higher order statistics previously have not been made available for general hysteresis models by using existing approximation methods. Second order moments obtained for the model by this non-Gaussian closure scheme are compared with equivalent linearization and Gaussian closure results via Monte Carlo simulation (MCS). Higher order moments are compared with the simulation results. The study performed for a wide range of degradation parameters and input power spectral density ( PSD) levels shows that the non-Gaussian responses obtained by this approach are in better agreement with the MCS results than the linearized and Gaussian ones. This approximation technique can provide information on higher order moments for general hysteretic systems. This information is valuable in random vibration and the reliability analysis of hysteretically yielding structures.