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K.Y.Xu 1 K.A.Alnefaie 2 N.H.Abu-Hamdeh 2 K.H.Almitani 2 E.C.Aifantis 2,3(1 Department of Mechanics,Shanghai University,Shanghai 200444,China)(2 Department of Mechanical Engineering,King Abdulaziz University,Jeddah 21589,Saudi Arabia)(3 Lab of Mechanics and Materials,Polytechnic School,Aristotle University,Thessaloniki 54124,Greece)  
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.
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