Dynamic equations for a micropolar cylinder
Paper in proceedings, 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.
micropolar cylinder eigenfrequency series expansion asymptotic