Chaotic dynamics of structural members under regular periodic and white noise excitations

J. Awrejcewicz, A. V. Krysko, I. V. Papkova, N. P. Erofeev, V. A. Krysko

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

1 Citation (Scopus)

Abstract

In this work we study PDEs governing beam dynamics under the Timoshenko hypotheses as well as the initial and boundary conditions which are yielded by Hamilton’s variational principle. The analysed beam is subjected to both uniform transversal harmonic load and additive white Gaussian noise. The PDEs are reduced to ODEs by means of the finite difference method employing the finite differences of the second-order accuracy, and then they are solved using the 4th and 6th order Runge-Kutta methods. The numerical results are validated with the applied nodes of the beam partition. The so-called charts of the beam vibration types are constructed versus the amplitude and frequency of harmonic excitation as well as the white noise intensity. The analysis of numerical results is carried out based on a theoretical background on non-linear dynamical systems with the help of time series, phase portraits, Poincaré maps, power spectra, Lyapunov exponents as well as using different wavelet-based studies. A few novel non-linear phenomena are detected, illustrated and discussed. In particular, it has been detected that a transition from regular to chaotic beam vibrations without noise has been realised by the modified Ruelle-Takens-Newhouse scenario. Furthermore, it has been shown that in the studied cases, the additive white noise action has not qualitatively changed the mentioned route to chaotic dynamics.

Original languageEnglish
Title of host publicationNumerical Analysis and Its Applications - 6th International Conference, NAA 2016, Revised Selected Papers
PublisherSpringer Verlag
Pages25-32
Number of pages8
Volume10187 LNCS
ISBN (Print)9783319570983
DOIs
Publication statusPublished - 2017
Event6th International Conference on Numerical Analysis and Its Applications, NAA 2016 - Lozenetz, Bulgaria
Duration: 15 Jun 201622 Jun 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10187 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference6th International Conference on Numerical Analysis and Its Applications, NAA 2016
CountryBulgaria
CityLozenetz
Period15.6.1622.6.16

Keywords

  • Bifurcations
  • Chaos
  • Non-linear dynamics
  • Timoshenko beam
  • White Gauss noise

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Awrejcewicz, J., Krysko, A. V., Papkova, I. V., Erofeev, N. P., & Krysko, V. A. (2017). Chaotic dynamics of structural members under regular periodic and white noise excitations. In Numerical Analysis and Its Applications - 6th International Conference, NAA 2016, Revised Selected Papers (Vol. 10187 LNCS, pp. 25-32). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10187 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-57099-0_3