Dynamic Higher Order Functionally Graded Micropolar Plate Equations

Abstract

The work, described in this paper, considers the analysis and derivation of dynamical equations on rectangular functionally graded plates governed by micropolar continuum theory. The proposed method is based on a power series expansion of the displacement field, micro-rotation field and material parameters in the thickness coordinates 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 a systematic fashion to any order desired. 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. The fundamental eigenfrequency is obtained for the plate using different truncations orders of the present theory. Also various plots of mode shapes and stress distributions are compared for the fundamental eigenfrequency.