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Nonlinear Dynamics

, Volume 90, Issue 4, pp 2481–2494 | Cite as

Radially and axially symmetric motions of a class of transversely isotropic compressible hyperelastic cylindrical tubes

  • Ran Wang
  • Wen-zheng Zhang
  • Zhen-tao Zhao
  • Hong-wu Zhang
  • Xue-gang YuanEmail author
Original Paper

Abstract

In this paper, the radially and axially symmetric motions are examined for a hyperelastic cylindrical tube composed of a class of transversely isotropic compressible neo-Hookean materials about the radial direction. Firstly, a system of coupled nonlinear evolution equations describing the motions of the cylindrical tube is derived by Hamilton’s principle. Then the system is reduced to a system of nonlinear ordinary differential equations by the travelling wave transformations. According to the theory of planar dynamical systems, qualitative analyses on the solutions of the system are given in different parameter spaces. Specially, the influences of the material parameters on the qualitative and quantitative properties of the solutions are discussed. Two types of travelling wave solutions of the radially symmetric motion are obtained, including classical periodic travelling wave solutions and solitary wave solutions with the peak form. So does the axially symmetric motion, but solitary wave solutions with the valley form. Correspondingly, some numerical examples are shown.

Keywords

Hyperelastic cylindrical tube Transversely isotropic compressible neo-Hookean material Radially and axially symmetric motions Bounded travelling wave solutions 

Notes

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 11672069, 11702059, 11232003, 11672062); the Ph.D. Programs Foundation of Ministry of Education of China (No. 20130041110050); the Research Start-up Project Plan for Liaoning Doctors (No. 20141119); the Fundamental Research Funds for the Central Universities (No. DC201502050407, DC201502050203); 111 Project (B08014). The authors also appreciate the editor’s earnest work and three anonymous reviewers for their helpful comments on an earlier draft of this paper.

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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  • Ran Wang
    • 1
  • Wen-zheng Zhang
    • 2
  • Zhen-tao Zhao
    • 1
  • Hong-wu Zhang
    • 1
  • Xue-gang Yuan
    • 1
    • 2
    Email author
  1. 1.State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering MechanicsDalian University of TechnologyDalianPeople’s Republic of China
  2. 2.College of ScienceDalian Minzu UniversityDalianPeople’s Republic of China

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