Dynamic higher order micropolar plate equations
Paper in proceedings, 2013
This work considers the analysis and derivation of dynamical equations on rectangular plates 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 thickness coordinate of the plate. This assumption results in sets of equations of motion together with consistent sets of boundary conditions. These derived equations are hyperbolic and can be constructed in systematic fashion to any order desired. Hence it is believed that these sets of equations are asymptotically correct. The construction of the equation is systematized by the introduction of recursion relations which relates higher order displacement and micro-rotation terms with the lower order terms. Furthermore the equations can be divided into two categories of motions, namely extensional and flexural motion.
Results are only obtained for the flexural motion of the plate using different truncations orders of the present theory, comparisons are performed with the plate theory developed by Eringen and the exact theory for micropolar continuum. Numerical examples are presented for dispersion curves on an infinite plate for the three lowest flexural modes. The three lowest eigenfrequencies for a simply supported plate are presented for different truncation orders, Eringen's plate theory and the exact theory. Also various plots on mode shapes stress distributions are compared for a infinite plate vibrating with a fix frequency.