Chaotic dynamics of the size-dependent non-linear micro-beam model

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

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

In this work, a size-dependent model of a Sheremetev-Pelekh-Reddy-Levinson micro-beam is proposed and validated using the couple stress theory, taking into account large deformations. The applied Hamilton's principle yields the governing PDEs and boundary conditions. A comparison of statics and dynamics of beams with and without size-dependent components is carried out. It is shown that the proposed model results in significant, both qualitative and quantitative, changes in the nature of beam deformations, in comparison to the so far employed standard models. A novel scenario of transition from regular to chaotic vibrations of the size-dependent Sheremetev-Pelekh model, following the Pomeau-Manneville route to chaos, is also detected and illustrated, among others.

Original languageEnglish
Pages (from-to)1339-1351
Number of pages13
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume50
DOIs
Publication statusPublished - 1 Sep 2017

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Chaotic Dynamics
Dependent
Couple Stress
Hamilton's Principle
Large Deformation
Standard Model
Chaos
Vibration
Chaos theory
Model
Boundary conditions
Scenarios

Keywords

  • Chaos
  • Couple stress theory
  • Micro-beam
  • PDEs

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

Cite this

Chaotic dynamics of the size-dependent non-linear micro-beam model. / Krysko, A. V.; Awrejcewicz, J.; Pavlov, S. P.; Zhigalov, M. V.; Krysko, V. A.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 50, 01.09.2017, p. 1339-1351.

Research output: Contribution to journalArticle

Krysko, A. V. ; Awrejcewicz, J. ; Pavlov, S. P. ; Zhigalov, M. V. ; Krysko, V. A. / Chaotic dynamics of the size-dependent non-linear micro-beam model. In: Communications in Nonlinear Science and Numerical Simulation. 2017 ; Vol. 50. pp. 1339-1351.
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