Analysis of chaotic vibrations of flexible plates using fast fourier transforms and wavelets

J. Awrejcewicz, A. V. Krysko, I. E. Kutepov, N. A. Zagniboroda, M. V. Zhigalov, V. A. Krysko

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

In this paper chaotic vibrations of flexible plates of infinite length are studied. The Kirchhoff-Love hypotheses are used to derive the nondimensional partial differential equations governing the plate dynamics. The finite difference method (FDM) and finite element method (FEM) are applied to validate the numerical results. The numerical analysis includes both standard (time histories, fast Fourier Transform, phase portraits, Poincaré sections, Lyapunov exponents) as well as wavelet-based approaches. The latter one includes the so called Gauss 1, Gauss 8, Mexican Hat and Morlet wavelets. In particular, various plate dynamical regimes including the periodic, quasi-periodic, sub-harmonic, chaotic vibrations as well as bifurcations of the plate are illustrated and studied. In addition, the convergence of numerical results obtained via different wavelets is analyzed.

Original languageEnglish
Article number1340005
JournalInternational Journal of Structural Stability and Dynamics
Volume13
Issue number7
DOIs
Publication statusPublished - 1 Oct 2013

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Fast Fourier transform
Finite difference method
Fast Fourier transforms
Partial differential equations
Numerical analysis
Wavelets
Vibration
Finite element method
Gauss
Numerical Results
Phase Portrait
Subharmonics
Lyapunov Exponent
Difference Method
Numerical Analysis
Finite Difference
Bifurcation
Partial differential equation
Finite Element Method

Keywords

  • bifurcation
  • Chaos
  • fast Fourier transform
  • plates
  • wavelets

ASJC Scopus subject areas

  • Mechanical Engineering
  • Civil and Structural Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Building and Construction
  • Applied Mathematics

Cite this

Analysis of chaotic vibrations of flexible plates using fast fourier transforms and wavelets. / Awrejcewicz, J.; Krysko, A. V.; Kutepov, I. E.; Zagniboroda, N. A.; Zhigalov, M. V.; Krysko, V. A.

In: International Journal of Structural Stability and Dynamics, Vol. 13, No. 7, 1340005, 01.10.2013.

Research output: Contribution to journalArticle

Awrejcewicz, J. ; Krysko, A. V. ; Kutepov, I. E. ; Zagniboroda, N. A. ; Zhigalov, M. V. ; Krysko, V. A. / Analysis of chaotic vibrations of flexible plates using fast fourier transforms and wavelets. In: International Journal of Structural Stability and Dynamics. 2013 ; Vol. 13, No. 7.
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