Dynamic equations for a micropolar cylinder

Paper in proceeding, 2015

This work considers the analysis and derivation of dynamical equations of a solid cylinder governed by micropolar continuum theory. The proposed method is based on a power series expansion of the displacement field and micro-rotation field in the radial coordinate of the cylinder. This assumption results in sets of equations of motion together with sets of boundary conditions that are variationally consistent. These derived equations are hyperbolic and can be constructed in a systematic fashion to any order desired where the equations are asymptotically correct to all studied orders. The construction of the equations are systematized by the introduction of recursion relations that relate higher order displacement and micro-rotation terms to the lower order terms. Results are obtained for cylinders using different truncations orders of the present theory including higher order benchmark solutions. Numerical examples are presented for dispersion curves, eigenfrequencies with stress and displacement distribution plots for simply supported cylinders.