Chaotic Vibrations of a Nonlinear Viscoelastic Beam

J. Argyris, V. Belubekian, N. Ovakimyan, M. Minasyan

Research output: Contribution to journalArticlepeer-review

Abstract

The differential equation of motion of a nonlinear viscoelastic beam is established and is based on a novel and sophisticated stress-strain law for polymers. Applying this equation we examine a periodically forced oscillation of such a simply supported beam and search for possible chaotic responses. To this purpose we establish the Holmes-Melnikov boundary for the system. All further investigations are developed by means of a computer simulation. In this connection the authors examine critically the Poincaré mapping and the Lyapunov exponent techniques and distinguish in this way between chaotic and regular motion. A set of control parameters of the equation is found, for which either a chaotic or a regular motion can be generated, depending on the initial conditions and the corresponding basins of attraction. Thus, in this particular case two attractors of completely different nature-regular and chaotic, respectively-coexist in the phase space. The basins of attraction of the two attractors for a fixed instant of time are plotted, and appear to possess a very complex fractal geometry.

Original languageEnglish (US)
Pages (from-to)151-163
Number of pages13
JournalChaos, solitons and fractals
Volume7
Issue number2
DOIs
StatePublished - Feb 1996
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

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