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

Результат исследований: Материалы для книги/типы отчетовМатериалы для конференции

1 Цитирования (Scopus)

Аннотация

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.

Язык оригиналаАнглийский
Название основной публикацииNumerical Analysis and Its Applications - 6th International Conference, NAA 2016, Revised Selected Papers
ИздательSpringer Verlag
Страницы25-32
Число страниц8
Том10187 LNCS
ISBN (печатное издание)9783319570983
DOI
СостояниеОпубликовано - 2017
Событие6th International Conference on Numerical Analysis and Its Applications, NAA 2016 - Lozenetz, Болгария
Продолжительность: 15 июн 201622 июн 2016

Серия публикаций

НазваниеLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Том10187 LNCS
ISSN (печатное издание)0302-9743
ISSN (электронное издание)1611-3349

Конференция

Конференция6th International Conference on Numerical Analysis and Its Applications, NAA 2016
СтранаБолгария
ГородLozenetz
Период15.6.1622.6.16

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Fingerprint Подробные сведения о темах исследования «Chaotic dynamics of structural members under regular periodic and white noise excitations». Вместе они формируют уникальный семантический отпечаток (fingerprint).

Цитировать