Quantifying chaos of curvilinear beams via exponents

J. Awrejcewicz, V. A. Krysko, I. E. Kutepov, I. Yu Vygodchikova, A. V. Krysko

Research output: Contribution to journalReview article

5 Citations (Scopus)

Abstract

We propose a procedure for predicting the stability loss and transition into chaos of a network of oscillators lying on a curve, where each of the oscillators can move in two perpendicular directions. Dynamics of the coupled oscillators are governed by the sixth-order PDE, which is directly derived using the classical hypotheses of a curvilinear flexible beam movement theory. We apply FDM (Finite Difference Method) to reduce PDEs into ODEs, and the used number of spatial coordinate positions defines the number of involved oscillators approximating the dynamics of our continuous structural member (beam). Our procedure has a few advantages over the classical approaches, which has been illustrated and discussed. The proposed method has been validated for non-linear dynamical regimes by using the classical vibrational analysis (time histories, frequency power spectra and Poincaré maps).

Original languageEnglish
Pages (from-to)81-92
Number of pages12
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume27
Issue number1-3
DOIs
Publication statusPublished - 1 Jan 2015
Externally publishedYes

Fingerprint

Chaos theory
Chaos
Exponent
Structural members
Power spectrum
Finite difference method
Flexible Beam
Frequency Spectrum
Coupled Oscillators
Power Spectrum
Perpendicular
Difference Method
Finite Difference
Curve
History
Movement

Keywords

  • Beam
  • Chaos
  • Elasticity
  • Network of oscillators
  • Stability

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

Cite this

Quantifying chaos of curvilinear beams via exponents. / Awrejcewicz, J.; Krysko, V. A.; Kutepov, I. E.; Vygodchikova, I. Yu; Krysko, A. V.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 27, No. 1-3, 01.01.2015, p. 81-92.

Research output: Contribution to journalReview article

Awrejcewicz, J. ; Krysko, V. A. ; Kutepov, I. E. ; Vygodchikova, I. Yu ; Krysko, A. V. / Quantifying chaos of curvilinear beams via exponents. In: Communications in Nonlinear Science and Numerical Simulation. 2015 ; Vol. 27, No. 1-3. pp. 81-92.
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