Random response of integrable Duhem hysteretic systems under non-white excitation

Yiqing Ni, Z. G. Ying, J. M. Ko, W. Q. Zhu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

16 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1407-1419
Number of pages13
JournalInternational Journal of Non-Linear Mechanics
Issue number8
Publication statusPublished - 1 Dec 2002


  • Hysteretic system
  • Integrable Duhem model
  • Random response
  • Stochastic averaging method

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


Dive into the research topics of 'Random response of integrable Duhem hysteretic systems under non-white excitation'. Together they form a unique fingerprint.

Cite this