Chaotic dynamics of flexible beams driven by external white noise

J. Awrejcewicz, A. V. Krysko, I. V. Papkova, V. M. Zakharov, N. P. Erofeev, E. Yu Krylova, J. Mrozowski, V. A. Krysko

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Mathematical models of continuous structural members (beams, plates and shells) subjected to an external additive white noise are studied. The structural members are considered as systems with infinite number of degrees of freedom. We show that in mechanical structural systems external noise can not only lead to quantitative changes in the system dynamics (that is obvious), but also cause the qualitative, and sometimes surprising changes in the vibration regimes. Furthermore, we show that scenarios of the transition from regular to chaotic regimes quantified by Fast Fourier Transform (FFT) can lead to erroneous conclusions, and a support of the wavelet analysis is needed. We have detected and illustrated the modifications of classical three scenarios of transition from regular vibrations to deterministic chaos. The carried out numerical experiment shows that the white noise lowers the threshold for transition into spatio-temporal chaotic dynamics. A transition into chaos via the proposed modified scenarios developed in this work is sensitive to small noise and significantly reduces occurrence of periodic vibrations. Increase of noise intensity yields decrease of the duration of the laminar signal range, i.e., time between two successive turbulent bursts decreases. Scenario of transition into chaos of the studied mechanical structures essentially depends on the control parameters, and it can be different in different zones of the constructed charts (control parameter planes). Furthermore, we found an interesting phenomenon, when increase of the noise intensity yields surprisingly the vibrational characteristics with a lack of noisy effect (chaos is destroyed by noise and windows of periodicity appear).

Original languageEnglish
Pages (from-to)225-253
Number of pages29
JournalMechanical Systems and Signal Processing
Volume79
DOIs
Publication statusPublished - 19 Feb 2016

Fingerprint

White noise
Chaos theory
Structural members
Wavelet analysis
Fast Fourier transforms
Dynamical systems
Mathematical models
Experiments

Keywords

  • Beams
  • Fourier and wavelet analysis
  • Noise-induced transitions
  • Parametric vibrations

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Civil and Structural Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Computer Science Applications

Cite this

Awrejcewicz, J., Krysko, A. V., Papkova, I. V., Zakharov, V. M., Erofeev, N. P., Krylova, E. Y., ... Krysko, V. A. (2016). Chaotic dynamics of flexible beams driven by external white noise. Mechanical Systems and Signal Processing, 79, 225-253. https://doi.org/10.1016/j.ymssp.2016.02.043

Chaotic dynamics of flexible beams driven by external white noise. / Awrejcewicz, J.; Krysko, A. V.; Papkova, I. V.; Zakharov, V. M.; Erofeev, N. P.; Krylova, E. Yu; Mrozowski, J.; Krysko, V. A.

In: Mechanical Systems and Signal Processing, Vol. 79, 19.02.2016, p. 225-253.

Research output: Contribution to journalArticle

Awrejcewicz, J, Krysko, AV, Papkova, IV, Zakharov, VM, Erofeev, NP, Krylova, EY, Mrozowski, J & Krysko, VA 2016, 'Chaotic dynamics of flexible beams driven by external white noise', Mechanical Systems and Signal Processing, vol. 79, pp. 225-253. https://doi.org/10.1016/j.ymssp.2016.02.043
Awrejcewicz, J. ; Krysko, A. V. ; Papkova, I. V. ; Zakharov, V. M. ; Erofeev, N. P. ; Krylova, E. Yu ; Mrozowski, J. ; Krysko, V. A. / Chaotic dynamics of flexible beams driven by external white noise. In: Mechanical Systems and Signal Processing. 2016 ; Vol. 79. pp. 225-253.
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