Three Kinds of Nonlinear-Dispersive Waves in Finite Deformation Elastic Rods

ZHANG Shan-yuan; LIU Zhi-fang

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Article Navigation > Applied Mathematics and Mechanics > 2008 > 29(7): 825-832

ZHANG Shan-yuan, LIU Zhi-fang. Three Kinds of Nonlinear-Dispersive Waves in Finite Deformation Elastic Rods[J]. Applied Mathematics and Mechanics, 2008, 29(7): 825-832.

Citation:

ZHANG Shan-yuan, LIU Zhi-fang. Three Kinds of Nonlinear-Dispersive Waves in Finite Deformation Elastic Rods[J]. Applied Mathematics and Mechanics, 2008, 29(7): 825-832.

Citation:

ZHANG Shan-yuan, LIU Zhi-fang. Three Kinds of Nonlinear-Dispersive Waves in Finite Deformation Elastic Rods[J]. Applied Mathematics and Mechanics, 2008, 29(7): 825-832.

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Three Kinds of Nonlinear-Dispersive Waves in Finite Deformation Elastic Rods

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

Received Date: 2007-07-24
Rev Recd Date: 2008-05-22
Publish Date: 2008-07-15

Abstract

Abstract

On the basis of classical linear theory on longitudinal,torsional and flexural waves in thin elastic rods,taking finite deformation and dispersive effects into consideration,three kinds of nonlinear evolution equations were derived.Qualitative analyses of three kinds of nonlinear equation were completed.It is shown that these equations have homoclinic or heteroclinic orbits on the phase plane, which correspond to solitary wave or shock wave solution respectively.Based on the principle of homogeneous balance,these equations were resolved by Jacobi elliptic function expansion method.The results show that the existence of solitary wave solution and shock wave solution are possible under certain conditions.These conclusions are consistent with that of the qualitative analysis.
- elastic thin rod,
- finite deformation,
- dispersive effect,
- solitary wave,
- shock wave

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References(12)

References

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