Nonlinear Flexural Waves and Chaos Behavior in Finite-Deflection Timoshenko Beam

ZHANG Shan-yuan; LIU Zhi-fang

doi:10.3879/j.issn.1000-0887.2010.11.002

Volume 31 Issue 11

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ZHANG Shan-yuan, LIU Zhi-fang. Nonlinear Flexural Waves and Chaos Behavior in Finite-Deflection Timoshenko Beam[J]. Applied Mathematics and Mechanics, 2010, 31(11): 1276-1286. doi: 10.3879/j.issn.1000-0887.2010.11.002

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Nonlinear Flexural Waves and Chaos Behavior in Finite-Deflection Timoshenko Beam

doi: 10.3879/j.issn.1000-0887.2010.11.002

Institute of Applied Mechanics and Biomedical Engineering, Taiyuan University of Technology, Taiyuan 030024, P. R. China

Received Date: 1900-01-01
Rev Recd Date: 2010-09-03
Publish Date: 2010-11-15

Abstract

Abstract

On the basis of the theory of Timoshenko beam,taking into account finite-deflection and axial inertia,the nonlinear partial differential equations governing flexural waves in a beam were derived.When employing the method of the traveling wave solution,the nonlinear partial differential equations can be transformed into an ordinary differential equation by using certain integral skills.The qualitative analysis indicates that the corresponding dynamic system has heteroclinic orbit under certain condition.The exact periodic solution of nonlinear wave equation was obtained by means of Jacobi elliptic function expansion.When the modulus of Jacobi elliptic function m → 1 in the degenerate case,the shock wave solution was given.Further,small perturbations arising from damping and external load to original Hamilton's system are introduced and the threshold condition of the existence of transverse heteroclinic point is obtained by Melnikov's method.It is proved from this that the perturbed system has chaotic property under Smale horseshoe transform.
- Timoshenko beam,
- finite-deflection,
- shock wave,
- chaos motion,
- Jacobi elliptic function expansion,
- Melnikov function

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References(15)

References

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