Free vibration analyses of functionally graded plates based on improved refined shear and normal deformation theory considering thickness stretching effect using Airy stress function

In this paper, an improved refined shear and normal deformation theory is used in order to investigate the vibration behavior of functionally graded rectangular plates. In this theory, displacements of various points of plate are assumed to be due to in-plane displacements of the middle plane and transverse displacement. Transverse displacement is divided into three parts: bending, shear, and thickness stretching. Using the Airy stress function, corresponding to the compatibility equation, and employing the extended Hamilton's principle, in-plane displacements are omitted from the equations of motions. Thus, the proposed approach uses only three-unknowns in the displacement field. The results of vibration analysis using the proposed approach are in excellent agreement with three-dimensional and quasi-three-dimensional solutions containing a greater number of unknowns to consider the thickness stretching effect. Static and dynamic behavior of wide variety of thin and thick functionally graded plates can be studied using the proposed approach in which not only the number of variables is reduced, but also the contribution of bending, shear, and thickness stretching are completely clarified.