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Solitary waves in finite deformation elastic circular rod

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Abstract

A new nonlinear wave equation of a finite deformation elastic circular rod simultaneously introducing transverse inertia and shearing strain was derived by means of Hamilton principle. The nonlinear equation includes two nonlinear terms caused by finite deformation and double geometric dispersion effects caused by transverse inertia and transverse shearing strain. Nonlinear wave equation and corresponding truncated nonlinear wave equation were solved by the hyperbolic secant function finite expansion method. The solitary wave solutions of these nonlinear equations were obtained. The necessary condition of these solutions existence was given also.

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Authors and Affiliations

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

    Liu Zhi-fang Doctor  (刘志芳) & Zhang Shan-yuan  (张善元)

Authors
  1. Liu Zhi-fang Doctor  (刘志芳)
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  2. Zhang Shan-yuan  (张善元)
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Corresponding author

Correspondence to Liu Zhi-fang Doctor  (刘志芳).

Additional information

Communicated by WANG Yin-bang

Project supported by the National Natural Science Foundation of China (No. 10472076) and the Natural Science Foundation of Shanxi Province of China (No.2006021005)

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Liu, Zf., Zhang, Sy. Solitary waves in finite deformation elastic circular rod. Appl Math Mech 27, 1431–1437 (2006). https://doi.org/10.1007/s10483-006-1016-y

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  • DOI: https://doi.org/10.1007/s10483-006-1016-y

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2000 Mathematics Subject Classification

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