Chaotic vibrations of two-layered beams and plates with geometric, physical and design nonlinearities

J. Awrejcewicz, A. V. Krysko, V. V. Bochkarev, T. V. Babenkova, I. V. Papkova, J. Mrozowski

Результат исследований: Материалы для журналаСтатья

6 Цитирования (Scopus)

Выдержка

In this paper, the theory of nonlinear interaction of two-layered beams and plates taking into account design, geometric and physical nonlinearities is developed. The theory is mainly developed relying on the first approximation of the EulerBernoulli hypothesis. Winkler type relation between clamping and contact pressure is applied allowing the contact pressure to be removed from the quantities being sought. Strongly nonlinear partial differential equations are solved using the finite difference method regarding space and time coordinates. On each time step the iteration procedure, which improves the contact area between the beams is applied and also the method of changeable stiffness parameters is used. A computational example regarding dynamic interaction of two beams depending on a gap between the beams is given. Each beam is subjected to transversal sign-changeable load, and the upper beam is hinged, whereas the bottom beam is clamped. It has been shown that for some fixed system parameters and with an increase of the external load amplitude, synchronization between two beams occurs with the upper beam vibration frequency. Qualitative analysis of the interaction of two noncoupled beams is also extended to the study of noncoupled plates. Charts of beam vibration types versus control parameters {q0, ωp}, i.e. the frequency and amplitude of excitation are constructed. Similar and previously described competitions have been reported in the case of two-layered plates.

Язык оригиналаАнглийский
Страницы (с-по)2837-2851
Число страниц15
ЖурналInternational Journal of Bifurcation and Chaos
Том21
Номер выпуска10
DOI
СостояниеОпубликовано - 1 янв 2011
Опубликовано для внешнего пользованияДа

Отпечаток

Vibration
Nonlinearity
Finite difference method
Partial differential equations
Synchronization
Stiffness
Contact
Design
Geometric Design
Nonlinear Interaction
Qualitative Analysis
Interaction
Chart
Nonlinear Partial Differential Equations
Control Parameter
Difference Method
Finite Difference
Excitation
Iteration
Approximation

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics

Цитировать

Chaotic vibrations of two-layered beams and plates with geometric, physical and design nonlinearities. / Awrejcewicz, J.; Krysko, A. V.; Bochkarev, V. V.; Babenkova, T. V.; Papkova, I. V.; Mrozowski, J.

В: International Journal of Bifurcation and Chaos, Том 21, № 10, 01.01.2011, стр. 2837-2851.

Результат исследований: Материалы для журналаСтатья

Awrejcewicz, J. ; Krysko, A. V. ; Bochkarev, V. V. ; Babenkova, T. V. ; Papkova, I. V. ; Mrozowski, J. / Chaotic vibrations of two-layered beams and plates with geometric, physical and design nonlinearities. В: International Journal of Bifurcation and Chaos. 2011 ; Том 21, № 10. стр. 2837-2851.
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