Acta Mechanica Solida Sinica

, Volume 26, Issue 1, pp 9–20 | Cite as

Dynamic Analysis of a Gradient Elastic Polymeric Fiber

  • K. Y. Xu
  • K. A. Alnefaie
  • N. H. Abu-Hamdeh
  • K. H. Almitani
  • E. C. Aifantis
Article

Abstract

A dynamic analysis of an elastic gradient-dependent polymeric fiber subjected to a periodic excitation is considered. A nonlinear gradient elasticity constitutive equation with strain-dependent gradient coefficients is first derived and the dispersive wave propagation properties for its linearized counterpart are briefly discussed. For the linearized problem a variational formulation is also developed to obtain related boundary conditions of both classical (standard) and non-classical (gradient) type. Analytical solutions in the form of Fourier series for the fiber’s displacement and strain fields are provided. The solutions depend on a dimensionless scale parameter (the diameter to length radio d = D/L) and, therefore, size effects are captured.

Key words

gradient elasticity polymeric fibers periodic excitations size effects 

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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2013

Authors and Affiliations

  • K. Y. Xu
    • 1
  • K. A. Alnefaie
    • 2
  • N. H. Abu-Hamdeh
    • 2
  • K. H. Almitani
    • 2
  • E. C. Aifantis
    • 2
    • 3
    • 4
  1. 1.Department of MechanicsShanghai UniversityShanghaiChina
  2. 2.Department of Mechanical EngineeringKing Abdulaziz UniversityJeddahSaudi Arabia
  3. 3.Lab of Mechanics and Materials, Polytechnic SchoolAristotle UniversityThessalonikiGreece
  4. 4.King Abdulaziz UniversityJeddahSaudi Arabia

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