Chaotic vibrations of closed cylindrical shells in a temperature field

A. V. Krysko, J. Awrejcewicz, E. S. Kuznetsova, V. A. Krysko

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

A closed cylindrical shell with circular cross-section having constant stiffness and density and subjected to sign changeable loading and embedded into a temperature field is analyzed. Both BubnovGalerkin (with a higher approximation) and Fourier methods are applied to solve the derived nonlinear nondimensional partial differential equations. Among others, the novel scenario of transition from shell harmonic to chaotic vibrations via the collapse of quasi-periodic vibrations with one independent frequency and Hopf bifurcation is detected, illustrated and discussed. In addition, it is shown how for various intensities of the temperature field (including its absence) the increase of the loading yields qualitative changes in the investigated shell dynamics, and how chaotic zones are transmitted into periodic ones and vice versa.

Original languageEnglish
Pages (from-to)1515-1529
Number of pages15
JournalInternational Journal of Bifurcation and Chaos
Volume18
Issue number5
DOIs
Publication statusPublished - 1 Jan 2008
Externally publishedYes

Fingerprint

Cylindrical Shell
Temperature Field
Shell
Temperature distribution
Vibration
Closed
Fourier Method
Hopf bifurcation
Nonlinear Partial Differential Equations
Approximation Methods
Hopf Bifurcation
Partial differential equations
Stiffness
Cross section
Harmonic
Scenarios

Keywords

  • Bubnov-Galerkin method
  • Chaos
  • Cylindrical shell
  • Fourier representation
  • Partial differential equations
  • Temperature field
  • Vibrations

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics

Cite this

Chaotic vibrations of closed cylindrical shells in a temperature field. / Krysko, A. V.; Awrejcewicz, J.; Kuznetsova, E. S.; Krysko, V. A.

In: International Journal of Bifurcation and Chaos, Vol. 18, No. 5, 01.01.2008, p. 1515-1529.

Research output: Contribution to journalArticle

Krysko, A. V. ; Awrejcewicz, J. ; Kuznetsova, E. S. ; Krysko, V. A. / Chaotic vibrations of closed cylindrical shells in a temperature field. In: International Journal of Bifurcation and Chaos. 2008 ; Vol. 18, No. 5. pp. 1515-1529.
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