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. theory, displacements various points plate are assumed be due in-plane middle plane transverse displacement. Transverse displacement divided into three parts: bending, shear, thickness stretching. Using Airy stress function, corresponding compatibility equation, employing extended Hamilton’s principle, omitted from equations motions. Thus, proposed approach uses only three-unknowns field. The results analysis using excellent agreement with three-dimensional quasi-three-dimensional solutions containing a greater number unknowns consider stretching effect. Static dynamic wide variety thin thick plates can studied which not variables reduced, but also contribution completely clarified.