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 journalArticle

18 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

Fingerprint

Functionally graded materials
Numerical analysis
Differential equations
Neural networks

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

Cite this

Chaotic dynamics of size dependent Timoshenko beams with functionally graded properties along their thickness. / Awrejcewicz, J.; Krysko, A. V.; Pavlov, S. P.; Zhigalov, M. V.; Krysko, V. A.

In: Mechanical Systems and Signal Processing, Vol. 93, 01.09.2017, p. 415-430.

Research output: Contribution to journalArticle

@article{26cbffa078c849e9a52984ec53fe319b,
title = "Chaotic dynamics of size dependent Timoshenko beams with functionally graded properties along their thickness",
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 K{\'a}rm{\'a}n 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.",
keywords = "Chaos, Fourier spectra, Lyapunov exponents, Modified couple stress theory, Nonlinear dynamics, Nonlinear Timoshenko beam, Wavelet",
author = "J. Awrejcewicz and Krysko, {A. V.} and Pavlov, {S. P.} and Zhigalov, {M. V.} and Krysko, {V. A.}",
year = "2017",
month = "9",
day = "1",
doi = "10.1016/j.ymssp.2017.01.047",
language = "English",
volume = "93",
pages = "415--430",
journal = "Mechanical Systems and Signal Processing",
issn = "0888-3270",
publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Chaotic dynamics of size dependent Timoshenko beams with functionally graded properties along their thickness

AU - Awrejcewicz, J.

AU - Krysko, A. V.

AU - Pavlov, S. P.

AU - Zhigalov, M. V.

AU - Krysko, V. A.

PY - 2017/9/1

Y1 - 2017/9/1

N2 - 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.

AB - 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.

KW - Chaos

KW - Fourier spectra

KW - Lyapunov exponents

KW - Modified couple stress theory

KW - Nonlinear dynamics

KW - Nonlinear Timoshenko beam

KW - Wavelet

UR - http://www.scopus.com/inward/record.url?scp=85015317659&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85015317659&partnerID=8YFLogxK

U2 - 10.1016/j.ymssp.2017.01.047

DO - 10.1016/j.ymssp.2017.01.047

M3 - Article

VL - 93

SP - 415

EP - 430

JO - Mechanical Systems and Signal Processing

JF - Mechanical Systems and Signal Processing

SN - 0888-3270

ER -