Control and dynamics of a SDOF system with piecewise linear stiffness and combined external excitations

D. Yurchenko, R. Iwankiewicz, P. Alevras

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The paper considers a problem of stochastic control and dynamics of a single-degree-of-freedom system with piecewise linear stiffness subjected to combined periodic and white noise external excitations. To minimize the system response energy a bounded in magnitude control force is applied to the systems. The stochastic optimal control problem is handled through the dynamic programming approach. Based on the solution to the Hamilton-Jacobi-Bellman equation it is proposed to use the dry friction control law in the non-resonant case. In the resonant case the stochastic averaging procedure has been used to derive stochastic differential equations for system response amplitude and phase. The joint PDF of response amplitude and phase is derived analytically and numerically using the Path Integration approach. (C) 2013 Elsevier Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)118-124
Number of pages7
JournalProbabilistic Engineering Mechanics
Volume35
DOIs
Publication statusPublished - Jan 2014

Keywords

  • Stochastic optimal control
  • Hamilton-Jacobi-Bellman equation
  • Fokker-Plank-Kolmogorov equation
  • Path integration method
  • Stochastic averaging
  • Piecewise linear
  • STRONGLY NONLINEAR OSCILLATORS
  • WHITE-NOISE EXCITATIONS
  • OPTIMAL BOUNDED CONTROL

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