A rational derivation of dynamic higher order equations for functionally graded micropolar plates

The dynamics of functionally graded micropolar plates is considered. The derivation process is based on power series expansions in the thickness coordinate. Using the three-dimensional equations of motion for micropolar continuum, variationally consistent equations of motion and end boundary conditions are derived in a systematic fashion up to arbitrary order. Numerical results are presented for simply supported plates using different material distributions for both low and high order truncation orders. These results illustrate that the present approach renders benchmark solutions provided higher order truncations are used, and act as engineering plate equations using low order truncation.