Complex parametric vibrations of flexible rectangular plates

J. Awrejcewicz, V. A. Krysko, A. V. Krysko

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)


In this paper we consider parametric oscillations of flexible plates within the model of von Kármán equations. First we propose the general iterational method to find solutions to even more general problem governed by the von Kármán-Vlasov-Mushtari equations. In the language of physics the found solutions define stress-strain state of flexible shallow shell with a bounded convex space Ω ∈ R2 and with sufficiently smooth boundary Γ. The new variational formulation of the problem has been proposed and his validity and application has been discussed using precise mathematical treatment. Then, using the earlier introduced theoretical results, an effective algorithm has been applied to convert problem of finding solutions to hybrid type partial differential equations of von Kármán form to that of the ordinary differential (ODEs) and algebraic (AEs) equations. Mechanisms of transition to chaos of deterministic systems with infinite number of degrees of freedom are presented. Comparison of mechanisms of transition to chaos with known ones is performed. The following cases of longitudinal loads of different sign are investigated: parametric load acting along X direction only, and parametric load acting in both directions X and Y with the same amplitude and frequency.

Original languageEnglish
Pages (from-to)221-244
Number of pages24
Issue number3
Publication statusPublished - 1 Jun 2004
Externally publishedYes


  • Chaos
  • Flexible plates
  • Parametric vibrations
  • Periodic and quasi-periodic motion
  • Von Kármán equations

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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