On the wavelet transform application to a study of chaotic vibrations of the infinite length flexible panels driven longitudinally

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

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

Both classical Fourier analysis and continuous wavelets transformation are applied to study non-linear vibrations of infinitely long flexible panels subject to longitudinal sign-changeable external load actions. First the governing PDEs are derived and then the BubnovGalerkin method is applied to yield 2N first order ODEs. The further used Lyapunov exponent computation is described. Transition scenarios from regular to chaotic dynamics of the being investigated plate strip are analyzed using different wavelets, and their suitability and advantages/disadvantages to nonlinear dynamics monitoring and quantifying are illustrated and discussed. A few novel results devoted to the beam nonlinear dynamics behavior are reported. In addition, links between the largest Lyapunov exponent computation and the wavelet spectrum numerical estimation are also illustrated and discussed.

Original languageEnglish
Pages (from-to)3347-3371
Number of pages25
JournalInternational Journal of Bifurcation and Chaos
Volume19
Issue number10
DOIs
Publication statusPublished - 1 Jan 2009

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Wavelet transforms
Wavelet Transform
Nonlinear Dynamics
Wavelets
Vibration
Wavelet Transformation
Largest Lyapunov Exponent
Nonlinear Vibration
Fourier Analysis
Chaotic Dynamics
Lyapunov Exponent
Dynamic Behavior
Strip
Fourier analysis
Monitoring
First-order
Scenarios

Keywords

  • Chaos
  • Plate strip
  • Stability
  • Wavelets

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics

Cite this

On the wavelet transform application to a study of chaotic vibrations of the infinite length flexible panels driven longitudinally. / Awrejcewicz, J.; Krysko, A. V.; Soldatov, V.

In: International Journal of Bifurcation and Chaos, Vol. 19, No. 10, 01.01.2009, p. 3347-3371.

Research output: Contribution to journalArticle

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