Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/9023
Title: Random response of integrable Duhem hysteretic systems under non-white excitation
Authors: Ni, YQ 
Ying, ZG
Ko, JM
Zhu, WQ
Keywords: Hysteretic system
Integrable Duhem model
Random response
Stochastic averaging method
Issue Date: 2002
Publisher: Pergamon-Elsevier Science Ltd
Source: International journal of non-linear mechanics, 2002, v. 37, no. 8, p. 1407-1419 How to cite?
Journal: International Journal of Non-Linear Mechanics 
Abstract: In this study, an integrable Duhem hysteresis model is derived from the mathematical Duhem operator. This model can represent a wide category of hysteretic systems. The stochastic averaging method of energy envelope is then adapted for response analysis of the integrable Duhem hysteretic system subjected to non-white random excitation. Using the integrability of the proposed model, potential energy and dissipated energy of the hysteretic system can be represented in an integration form so that the hysteretic restoring force is separable into conservative and dissipative parts. Based on the equivalence of dissipated energy, a non-hysteretic non-linear system is obtained to substitute the original system, and the averaged Itô stochastic differential equation of total energy is derived with the drift and diffusion coefficients being expressed as Fourier series expansions in space averaging. The stationary probability density of total energy and response statistics are obtained by solving the Fokker-Planck-Kolmogorov (FPK) equation associated with the Itô equation. Verification is given by comparing the computational results with Monte Carlo simulations.
URI: http://hdl.handle.net/10397/9023
ISSN: 0020-7462
DOI: 10.1016/S0020-7462(02)00026-4
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