On the lyapunov exponents computation of coupled non-linear euler-bernoulli beams

J. Awrejcewicz, A. V. Krysko, V. Dobriyan, I. V. Papkova, V. A. Krysko

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this work the mathematical modeling and analysis of the chaotic dynamics of flexible Euler-Bernoulli beams is carried out. The Karman-type geometric non-linearity is taken into account. The algorithms reducing the studied objects associated with the boundary value problems are to the Cauchy problem using the finite difference method (FDM) with an approximation of and the finite element method (FEM). The constructed Cauchy problem is solved using the fourth and six Runge-Kutta methods. The validity and reliability of the obtained results is rigorously discussed. We analyze time histories, phase and modal portraits, autocorrelation functions, the Poincarè and pseudo-Poincarè maps, signs of the first four Lyapunov exponents, as well as the compression factor of the phase volume of an attractor. In particular, we study a transition from symmetric to asymmetric vibrations, and we explain this phenomenon. Vibration-type charts are reported regarding two control parameters: The amplitude and the frequency of the uniformly distributed periodic excitation. Furthermore, we have detected and illustrated chaotic vibrations of the Euler-Bernoulli beams for different boundary conditions and different beam thicknesses. 2O(c).

Original languageEnglish
Title of host publicationProceedings of the 14th International Conference on Civil, Structural and Environmental Engineering Computing, CC 2013
PublisherCivil-Comp Press
Volume102
ISBN (Print)9781905088577
Publication statusPublished - 1 Jan 2013
Externally publishedYes
Event14th International Conference on Civil, Structural and Environmental Engineering Computing, CC 2013 - Cagliari, Sardinia, Italy
Duration: 3 Sep 20136 Sep 2013

Conference

Conference14th International Conference on Civil, Structural and Environmental Engineering Computing, CC 2013
CountryItaly
CityCagliari, Sardinia
Period3.9.136.9.13

Fingerprint

Runge Kutta methods
Autocorrelation
Finite difference method
Boundary value problems
Boundary conditions
Finite element method

Keywords

  • Attractors
  • Bifurcations
  • Chaotic vibrations
  • Phase portraits
  • Temporal-space chaos
  • The euler-bernoulli beams

ASJC Scopus subject areas

  • Environmental Engineering
  • Civil and Structural Engineering
  • Computational Theory and Mathematics
  • Artificial Intelligence

Cite this

Awrejcewicz, J., Krysko, A. V., Dobriyan, V., Papkova, I. V., & Krysko, V. A. (2013). On the lyapunov exponents computation of coupled non-linear euler-bernoulli beams. In Proceedings of the 14th International Conference on Civil, Structural and Environmental Engineering Computing, CC 2013 (Vol. 102). Civil-Comp Press.

On the lyapunov exponents computation of coupled non-linear euler-bernoulli beams. / Awrejcewicz, J.; Krysko, A. V.; Dobriyan, V.; Papkova, I. V.; Krysko, V. A.

Proceedings of the 14th International Conference on Civil, Structural and Environmental Engineering Computing, CC 2013. Vol. 102 Civil-Comp Press, 2013.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Awrejcewicz, J, Krysko, AV, Dobriyan, V, Papkova, IV & Krysko, VA 2013, On the lyapunov exponents computation of coupled non-linear euler-bernoulli beams. in Proceedings of the 14th International Conference on Civil, Structural and Environmental Engineering Computing, CC 2013. vol. 102, Civil-Comp Press, 14th International Conference on Civil, Structural and Environmental Engineering Computing, CC 2013, Cagliari, Sardinia, Italy, 3.9.13.
Awrejcewicz J, Krysko AV, Dobriyan V, Papkova IV, Krysko VA. On the lyapunov exponents computation of coupled non-linear euler-bernoulli beams. In Proceedings of the 14th International Conference on Civil, Structural and Environmental Engineering Computing, CC 2013. Vol. 102. Civil-Comp Press. 2013
Awrejcewicz, J. ; Krysko, A. V. ; Dobriyan, V. ; Papkova, I. V. ; Krysko, V. A. / On the lyapunov exponents computation of coupled non-linear euler-bernoulli beams. Proceedings of the 14th International Conference on Civil, Structural and Environmental Engineering Computing, CC 2013. Vol. 102 Civil-Comp Press, 2013.
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