Chaotic dynamics of flexible euler-bernoulli beams

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

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

Mathematical modeling and analysis of spatio-temporal chaotic dynamics of flexible simple and curved Euler-Bernoulli beams are carried out. The Kármán-type geometric non-linearity is considered. Algorithms reducing partial differential equations which govern the dynamics of studied objects and associated boundary value problems are reduced to the Cauchy problem through both Finite Difference Method with the approximation of O(c2) and Finite Element Method. The obtained Cauchy problem is solved via the fourth and sixth-order Runge-Kutta methods. Validity and reliability of the results are rigorously discussed. Analysis of the chaotic dynamics of flexible Euler-Bernoulli beams for a series of boundary conditions is carried out with the help of the qualitative theory of differential equations. We analyze time histories, phase and modal portraits, autocorrelation functions, the Poincaré and pseudo-Poincaré maps, signs of the first four Lyapunov exponents, as well as the compression factor of the phase volume of an attractor. A novel scenario of transition from periodicity to chaos is obtained, and a transition from chaos to hyper-chaos is illustrated. In particular, we study and explain the phenomenon of transition from symmetric to asymmetric vibrations. Vibration-type charts are given regarding two control parameters: amplitude q0 and frequency ωp of the uniformly distributed periodic excitation. Furthermore, we detected and illustrated how the so called temporal-space chaos is developed following the transition from regular to chaotic system dynamics.

Original languageEnglish
Article number043130
JournalChaos
Volume23
Issue number4
DOIs
Publication statusPublished - 2 Oct 2013
Externally publishedYes

Fingerprint

Flexible Beam
Euler-Bernoulli beams
Euler-Bernoulli Beam
Chaotic Dynamics
Chaos theory
chaos
Chaos
Cauchy problem
Cauchy Problem
Vibration
Hyperchaos
Curved Beam
Geometric Nonlinearity
vibration
Runge-Kutta method
Runge Kutta methods
Chaotic systems
charts
Autocorrelation Function
Runge-Kutta Methods

ASJC Scopus subject areas

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

Cite this

Awrejcewicz, J., Krysko, A. V., Kutepov, I. E., Zagniboroda, N. A., Dobriyan, V., & Krysko, V. A. (2013). Chaotic dynamics of flexible euler-bernoulli beams. Chaos, 23(4), [043130]. https://doi.org/10.1063/1.4838955

Chaotic dynamics of flexible euler-bernoulli beams. / Awrejcewicz, J.; Krysko, A. V.; Kutepov, I. E.; Zagniboroda, N. A.; Dobriyan, V.; Krysko, V. A.

In: Chaos, Vol. 23, No. 4, 043130, 02.10.2013.

Research output: Contribution to journalArticle

Awrejcewicz, J, Krysko, AV, Kutepov, IE, Zagniboroda, NA, Dobriyan, V & Krysko, VA 2013, 'Chaotic dynamics of flexible euler-bernoulli beams', Chaos, vol. 23, no. 4, 043130. https://doi.org/10.1063/1.4838955
Awrejcewicz J, Krysko AV, Kutepov IE, Zagniboroda NA, Dobriyan V, Krysko VA. Chaotic dynamics of flexible euler-bernoulli beams. Chaos. 2013 Oct 2;23(4). 043130. https://doi.org/10.1063/1.4838955
Awrejcewicz, J. ; Krysko, A. V. ; Kutepov, I. E. ; Zagniboroda, N. A. ; Dobriyan, V. ; Krysko, V. A. / Chaotic dynamics of flexible euler-bernoulli beams. In: Chaos. 2013 ; Vol. 23, No. 4.
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