Contact interaction of flexible Timoshenko beams with small deflections

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....

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Bibliographic Details
Published in:Journal of physics. Conference series 2018-01, Vol.944 (1), p.12087
Main Authors: Papkova, I V, Krysko, A V, Saltykova, O A, Zakharova, A A, Krysko, V A
Format: Article
Language:English
Subjects:
Beams (structural)
chaos
Contact interaction
Dynamical systems
finite difference method
Geometric nonlinearity
Mathematical models
Nonlinear dynamics
Numerical analysis
Numerical methods
Ordinary differential equations
Partial differential equations
Physics
Qualitative analysis
Runge-Kutta method
Runge-Kutta type methods
Timoshenko beams
Timoshenko's beam
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Summary: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.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/944/1/012087