Investigations of chaotic dynamics of multi-layer beams taking into account rotational inertial effects

A. V. Krysko, J. Awrejcewicz, O. A. Saltykova, M. V. Zhigalov, V. A. Krysko

Research output: Contribution to journalReview article

22 Citations (Scopus)

Abstract

We propose a novel mathematical model of a vibrating multi-layer Timoshenko-type beam. We show that the introduced model essentially changes the type of partial differential equations allowing inclusion of rotational inertial effects. We illustrate and discuss the influence of boundary conditions, the beam layers and parameters of the external load on the non-linear dynamics of this composite beam including a study of its regular, bifurcation and chaotic behavior.The originally derived infinite problem is reduced to the finite one using either Finite Difference Method (FDM) or Finite Element Method (FEM) which guarantees validity and reliability of the obtained numerical results. In addition, a comparative study is carried out aiming at a proper choice of the efficient wavelet transform. In particular, scenarios of transition into chaos are studied putting emphasis on novel phenomena. Charts of the system dynamical regimes are also constructed with respect to the control parameters regarding thickness and composition of the beam layers.

Original languageEnglish
Pages (from-to)2568-2589
Number of pages22
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume19
Issue number8
DOIs
Publication statusPublished - 1 Aug 2014
Externally publishedYes

Fingerprint

Chaotic Dynamics
Finite difference method
Chaos theory
Wavelet transforms
Partial differential equations
Multilayer
Dynamical systems
Boundary conditions
Mathematical models
Finite element method
Composite materials
Chemical analysis
Composite Beams
Chaotic Behavior
Chart
Control Parameter
Wavelet Transform
Nonlinear Dynamics
Difference Method
Comparative Study

Keywords

  • Bifurcation
  • Chaos
  • Multi-layer Timoshenko beams
  • Wavelets

ASJC Scopus subject areas

  • Modelling and Simulation
  • Numerical Analysis
  • Applied Mathematics

Cite this

Investigations of chaotic dynamics of multi-layer beams taking into account rotational inertial effects. / Krysko, A. V.; Awrejcewicz, J.; Saltykova, O. A.; Zhigalov, M. V.; Krysko, V. A.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 19, No. 8, 01.08.2014, p. 2568-2589.

Research output: Contribution to journalReview article

Krysko, A. V. ; Awrejcewicz, J. ; Saltykova, O. A. ; Zhigalov, M. V. ; Krysko, V. A. / Investigations of chaotic dynamics of multi-layer beams taking into account rotational inertial effects. In: Communications in Nonlinear Science and Numerical Simulation. 2014 ; Vol. 19, No. 8. pp. 2568-2589.
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