Chaotic vibrations of flexible curvilinear beams in temperature and electric fields

J. Awrejcewicz, V. A. Krysko, I. E. Kutepov, N. A. Zagniboroda, V. Dobriyan, I. V. Papkova, A. V. Krysko

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this paper regular and chaotic vibrations of flexible curvilinear beams with (and without) the action of temperature and electric fields are studied. Results obtained are based on the reduction of PDEs governing non-linear dynamics of straight and curvilinear beams to large sets of non-linear ODEs putting emphasis on reliability and validation of the results. In spite of the applied classical approaches to study bifurcational and chaotic dynamics, we have employed 2D and 3D Morlet wavelets and we have computed first four Lyapunov exponents. Numerous results are reported regarding scenarios of the transition from regular to chaotic vibrations including the occurrence of hyper-hyper chaos and deep chaos. Snap-through phenomena have been detected and analyzed, and the influence of boundary conditions of three types of the considered fields (mechanical, thermal and electrical) as well as of temperature on non-linear dynamics of the beam have been reported.

Original languageEnglish
Pages (from-to)29-41
Number of pages13
JournalInternational Journal of Non-Linear Mechanics
Volume76
DOIs
Publication statusPublished - 30 May 2015
Externally publishedYes

Fingerprint

Temperature Field
Electric Field
Temperature distribution
Vibration
Electric fields
Chaos theory
Nonlinear Dynamics
Hyperchaos
Nonlinear ODE
Chaotic Dynamics
Large Set
Lyapunov Exponent
Straight
Chaos
Wavelets
Boundary conditions
Scenarios
Temperature

Keywords

  • Chaos
  • Curvilinear Euler-Bernoulli beams
  • Electric fields
  • Heat transfer equations
  • Lyapunov exponents

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Applied Mathematics

Cite this

Chaotic vibrations of flexible curvilinear beams in temperature and electric fields. / Awrejcewicz, J.; Krysko, V. A.; Kutepov, I. E.; Zagniboroda, N. A.; Dobriyan, V.; Papkova, I. V.; Krysko, A. V.

In: International Journal of Non-Linear Mechanics, Vol. 76, 30.05.2015, p. 29-41.

Research output: Contribution to journalArticle

Awrejcewicz, J. ; Krysko, V. A. ; Kutepov, I. E. ; Zagniboroda, N. A. ; Dobriyan, V. ; Papkova, I. V. ; Krysko, A. V. / Chaotic vibrations of flexible curvilinear beams in temperature and electric fields. In: International Journal of Non-Linear Mechanics. 2015 ; Vol. 76. pp. 29-41.
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AU - Zagniboroda, N. A.

AU - Dobriyan, V.

AU - Papkova, I. V.

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