Nonlinear behaviour of different flexible size-dependent beams models based on the modified couple stress theory. Part 2. Chaotic dynamics of flexible beams

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

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

In the present part of the paper various problems of non-linear dynamics of nano-beams within the modified couple stress theory as well as the Bernoulli-Euler, Timoshenko, and Sheremetev-Pelekh-Reddy-Levinson models are studied taking into account the geometric non-linearity. Different characteristics of the vibrational process, including Fourier spectra, wavelet spectra, phase portraits, Poincaré maps as well as the largest Lyapunov exponents, are studied for the same physical-geometric parameter with and without consideration of the size-dependent behaviour. Vibration graphs are constructed and analysed, and scenarios of transition from regular to chaotic vibrations are illustrated and discussed.

Original languageEnglish
Pages (from-to)106-121
Number of pages16
JournalInternational Journal of Non-Linear Mechanics
Volume93
DOIs
Publication statusPublished - 1 Jul 2017

Fingerprint

Flexible Beam
Couple Stress
Chaotic Dynamics
Vibration
Model-based
Fourier Spectrum
Geometric Nonlinearity
Largest Lyapunov Exponent
Dependent
Phase Portrait
Bernoulli
Nonlinear Dynamics
Euler
Wavelets
Scenarios
Graph in graph theory
Model

Keywords

  • Beam models
  • Chaos
  • Nano-mechanics
  • Vibrations

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Cite this

Nonlinear behaviour of different flexible size-dependent beams models based on the modified couple stress theory. Part 2. Chaotic dynamics of flexible beams. / Krysko, A. V.; Awrejcewicz, J.; Zhigalov, M. V.; Pavlov, S. P.; Krysko, V. A.

In: International Journal of Non-Linear Mechanics, Vol. 93, 01.07.2017, p. 106-121.

Research output: Contribution to journalArticle

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