Dynamic analysis of a gradient elastic polymeric fiber

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 fiberʹs 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.