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

Результат исследований: Материалы для журналаСтатьярецензирование

34 Цитирования (Scopus)

Аннотация

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.

Язык оригиналаАнглийский
Страницы (с-по)415-430
Число страниц16
ЖурналMechanical Systems and Signal Processing
Том93
DOI
СостояниеОпубликовано - 1 сен 2017

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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