Spatio-temporal chaos and solitons exhibited by von Kármán model

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

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

Forced oscillations of flexible plates with a longitudinal, time dependent load acting on one plate side are investigated. Regular (harmonic, subharmonic and quasi-periodic) and irregular (chaotic) oscillations appear depending on the system parameters as well as initial and boundary conditions. In order to achieve highly reliable results, an effective algorithm has been applied to convert a problem of finding solutions to the hybrid type partial differential equations (the so-called von Kármán form) to that of the ordinary differential equations (ODEs) and algebraic equations (AEs). The obtained equations are solved using finite difference method with the approximations 0(h4) and 0(h2) (in respect to the spatial coordinates). The ODEs are solved using the Runge-Kutta fourth order method, whereas the AEs are solved using either the Gauss or relaxation methods. The analysis and identification of spatio-temporal oscillations are carried out by investigation of the series wij(t), wt,ij(t), phase portraits wt,ij(wij) and wtt,ij(wt,ij wij) and the mode portraits in the planes wx,ij(wij), wy,ij(wij) and in the space wxx(wx,ij, wij), FFT as well as the Poincaré sections and pseudo-sections.

Original languageEnglish
Pages (from-to)1465-1513
Number of pages49
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume12
Issue number7
DOIs
Publication statusPublished - 1 Jan 2002
Externally publishedYes

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Spatiotemporal Chaos
Solitons
Ordinary differential equations
Algebraic Equation
Chaos theory
Ordinary differential equation
Oscillation
Forced oscillation
Relaxation Method
Phase Portrait
Subharmonics
Runge-Kutta
Finite difference method
Fast Fourier transforms
Gauss
Partial differential equations
Difference Method
Convert
Fourth Order
Irregular

Keywords

  • Chaos
  • Partial and ordinary differential equations
  • Plate
  • Soliton
  • Von Kármán model

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics

Cite this

Spatio-temporal chaos and solitons exhibited by von Kármán model. / Awrejcewicz, J.; Krysko, V. A.; Krysko, A. V.

In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 12, No. 7, 01.01.2002, p. 1465-1513.

Research output: Contribution to journalArticle

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