Solitary Waves and Chaotic Behavior in Large-Deflection Beam

Yi Qing Zhou; Zhi Fang Liu; Shan Yuan Zhang

doi:10.4028/www.scientific.net/AMM.29-32.28

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 29-32Solitary Waves and Chaotic Behavior in...

Solitary Waves and Chaotic Behavior in Large-Deflection Beam

Abstract:

The motion equation of nonlinear flexural wave in large-deflection beam is derived from Hamilton's variational principle using the coupling of flexural deformation and midplane stretching as key source of nonlinearity and taking into account transverse, axial and rotary inertia effects. The system has homoclinic or heteroclinic orbit under certain conditions, the exact periodic solutions of nonlinear wave equation are obtained by means of Jacobi elliptic function expansion. The solitary wave solution and shock wave solution is given when the modulus of Jacobi elliptic function in the degenerate case. It is easily thought that the introduction of damping and external load can result in break of homoclinic (or heteroclinic) orbit and appearance of transverse homoclinic point. The threshold condition of the existence of transverse homoclinic point is given by help of Melnikov function. It shows that the system has chaos property under Smale horseshoe meaning.

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Periodical:

Applied Mechanics and Materials (Volumes 29-32)

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28-34

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.29-32.28

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Online since:

August 2010

Authors:

Yi Qing Zhou, Zhi Fang Liu, Shan Yuan Zhang

Keywords:

Chaotic Motion, Finite-Deflection Beam, Jacobi Elliptic Function Expansion, Melnikov Function, Solitary Wave

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