Contact interaction of flexible Timoshenko beams with small deflections

I. V. Papkova, A. V. Krysko, O. A. Saltykova, A. A. Zakharova, V. A. Krysko

Research output: Contribution to journalConference article

Abstract

In this work chaotic dynamics contact interaction of two flexible Tymoshenko beams, under the action of a transversal alternating load is investigated. The contact interaction of the beams is taken into account by the Kantor model. The geometric nonlinearity is taken into account by the model of T. von Karman. The system of partial differential equations of the twelfth order reduces to the system of ordinary differential equations by the method of finite differences of the second order. The resulting system by methods of Runge-Kutta type of the second, fourth and eighth orders was solved. Our theoretical/numerical analysis is supported by methods of nonlinear dynamics and the qualitative theory of differential equations. Chaotic vibrations of two flexible beams of Timoshenko were investigated and the optimal step values over the spatial coordinate and the time steps for the numerical experiment were found. Convergence for all applicable numerical methods have been achieved and shown that chaotic signals are true.

Original languageEnglish
Article number012087
JournalJournal of Physics: Conference Series
Volume944
Issue number1
DOIs
Publication statusPublished - 30 Jan 2018
Event11th International Scientific and Technical Conference on Applied Mechanics and Dynamics Systems, AMSD 2017 - Omsk, Russian Federation
Duration: 14 Nov 201716 Nov 2017

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Timoshenko beams
deflection
electric contacts
differential equations
interactions
partial differential equations
numerical analysis
nonlinearity
vibration

Keywords

  • chaos
  • Contact interaction
  • finite difference method
  • geometric nonlinearity
  • Runge-Kutta type methods
  • Timoshenko's beam

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Contact interaction of flexible Timoshenko beams with small deflections. / Papkova, I. V.; Krysko, A. V.; Saltykova, O. A.; Zakharova, A. A.; Krysko, V. A.

In: Journal of Physics: Conference Series, Vol. 944, No. 1, 012087, 30.01.2018.

Research output: Contribution to journalConference article

Papkova, I. V. ; Krysko, A. V. ; Saltykova, O. A. ; Zakharova, A. A. ; Krysko, V. A. / Contact interaction of flexible Timoshenko beams with small deflections. In: Journal of Physics: Conference Series. 2018 ; Vol. 944, No. 1.
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AU - Papkova, I. V.

AU - Krysko, A. V.

AU - Saltykova, O. A.

AU - Zakharova, A. A.

AU - Krysko, V. A.

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N2 - In this work chaotic dynamics contact interaction of two flexible Tymoshenko beams, under the action of a transversal alternating load is investigated. The contact interaction of the beams is taken into account by the Kantor model. The geometric nonlinearity is taken into account by the model of T. von Karman. The system of partial differential equations of the twelfth order reduces to the system of ordinary differential equations by the method of finite differences of the second order. The resulting system by methods of Runge-Kutta type of the second, fourth and eighth orders was solved. Our theoretical/numerical analysis is supported by methods of nonlinear dynamics and the qualitative theory of differential equations. Chaotic vibrations of two flexible beams of Timoshenko were investigated and the optimal step values over the spatial coordinate and the time steps for the numerical experiment were found. Convergence for all applicable numerical methods have been achieved and shown that chaotic signals are true.

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