A unified formulation for free vibration of functionally graded plates

A simple, accurate, and unified formulation for the free vibration analysis of functionally graded (FG) plates is introduced. New four-variable first-order and higher-order shear deformation theories together with the classical FG plate theory can be easily achieved. The only assumption is that the transverse displacement consists of bending and shear components, and hence the theory has the potential to be used for modeling of the nonlinear FG plate problems. To validate the proposed formulation, the free vibration analysis of FG plates on two-parameter elastic foundation is conducted. The material properties vary continuously through the plate thickness. Analytical solutions for simply supported and approximate solutions for FG plates with arbitrary boundary conditions are extracted by extending the application of the conventional differential quadrature method as an accurate and efficient numerical tool. Comparison studies with existing two- and three-dimensional results available in open literature are performed. Excellent agreement between the results of the present formulation and the other theories is observed.