Geometrical Nonlinear Waves in Finite Deformation Elastic Rods

GUO Jian-gang; ZHOU Li-jun; ZHANG Shan-yuan

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Article Navigation > Applied Mathematics and Mechanics > 2005 > 26(5): 614-620

GUO Jian-gang, ZHOU Li-jun, ZHANG Shan-yuan. Geometrical Nonlinear Waves in Finite Deformation Elastic Rods[J]. Applied Mathematics and Mechanics, 2005, 26(5): 614-620.

Citation:

GUO Jian-gang, ZHOU Li-jun, ZHANG Shan-yuan. Geometrical Nonlinear Waves in Finite Deformation Elastic Rods[J]. Applied Mathematics and Mechanics, 2005, 26(5): 614-620.

Citation:

GUO Jian-gang, ZHOU Li-jun, ZHANG Shan-yuan. Geometrical Nonlinear Waves in Finite Deformation Elastic Rods[J]. Applied Mathematics and Mechanics, 2005, 26(5): 614-620.

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Geometrical Nonlinear Waves in Finite Deformation Elastic Rods

1.
Institute of Applied Mechanics, Taiyuan University of Technology, Taiyuan 030024, P. R. China;

Received Date: 2004-06-04
Rev Recd Date: 2004-11-30
Publish Date: 2005-05-15

Abstract

Abstract

By usinge Hamilton-type variation principle in non-conservation system, the nonlinear equation of wave motion of a elastic thin rod was derived according to Lagrange description of finite deformation theory. The dissipation caused due to viscous effect and the dispersion introduced by transverse inertia were taken into consideration so that steady traveling wave solution can be obtained. Using multi-scale method the nonlinear equation is reduced to a KdV-Burgers equation which corresponds with saddle-spiral heteroclinic orbit on phase plane. Its solution is called the oscillating-solitary wave or saddle-spiral shock wave. If viscous effect or transverse inertia is neglected, the equation is degraded to classical KdV or Burgers equation. The former implies a propagating solitary wave with homoclinic on phase plane, the latter means shock wave and heteroclinic orbit.
- nonlinear wave,
- finite deformation,
- viscous effect,
- transverse inertia effect,
- multi-scale method

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References(8)

References

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