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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.
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 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. a dimensionless scale parameter (the diameter to length radio d = D / L) and, therefore, size effects are captured.