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Acta Mechanica Solida Sinica

, Volume 19, Issue 1, pp 1–8 | Cite as

Nonlinear waves and periodic solution in finite deformation elastic rod

  • Zhifang Liu
  • Shanyuan Zhang
Article

Abstract

A nonlinear wave equation of elastic rod taking account of finite deformation, transverse inertia and shearing strain is derived by means of the Hamilton principle in this paper. Nonlinear wave equation and truncated nonlinear wave equation are solved by the Jacobi elliptic sine function expansion and the third kind of Jacobi elliptic function expansion method. The exact periodic solutions of these nonlinear equations are obtained, including the shock wave solution and the solitary wave solution. The necessary condition of exact periodic solutions, shock solution and solitary solution existence is discussed.

Key words

nonlinear wave finite deformation Poisson effect Jacobi elliptic function 

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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2006

Authors and Affiliations

  • Zhifang Liu
    • 1
  • Shanyuan Zhang
    • 1
  1. 1.Institute of Applied MechanicsTaiyuan University of TechnologyTaiyuanChina

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