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

20 Citations (Scopus)


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
Publication statusPublished - 1 Jul 2017



  • Beam models
  • Chaos
  • Nano-mechanics
  • Vibrations

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Cite this