Chaotic dynamics of size dependent Timoshenko beams with functionally graded properties along their thickness

J. Awrejcewicz, A. V. Krysko, S. P. Pavlov, M. V. Zhigalov, V. A. Krysko

Research output: Contribution to journalArticlepeer-review

34 Citations (Scopus)

Abstract

Chaotic dynamics of microbeams made of functionally graded materials (FGMs) is investigated in this paper based on the modified couple stress theory and von Kármán geometric nonlinearity. We assume that the beam properties are graded along the thickness direction. The influence of size-dependent and functionally graded coefficients on the vibration characteristics, scenarios of transition from regular to chaotic vibrations as well as a series of static problems with an emphasis put on the load-deflection behavior are studied. Our theoretical/numerical analysis is supported by methods of nonlinear dynamics and the qualitative theory of differential equations supplemented by Fourier and wavelet spectra, phase portraits, and Lyapunov exponents spectra estimated by different algorithms, including Wolf's, Rosenstein's, Kantz's, and neural networks. We have also detected and numerically validated a general scenario governing transition into chaotic vibrations, which follows the classical Ruelle-Takens-Newhouse scenario for the considered values of the size-dependent and grading parameters.

Original languageEnglish
Pages (from-to)415-430
Number of pages16
JournalMechanical Systems and Signal Processing
Volume93
DOIs
Publication statusPublished - 1 Sep 2017

Keywords

  • Chaos
  • Fourier spectra
  • Lyapunov exponents
  • Modified couple stress theory
  • Nonlinear dynamics
  • Nonlinear Timoshenko beam
  • Wavelet

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Civil and Structural Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Computer Science Applications

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