In this paper, an approach based on the refined plate theory and Airy stress function has been proposed to investigate the vibration and buckling behaviors of functionally graded (FG) rectangular plates. The significant feature of the proposed approach is considering only two unknowns in the displacement field in which the contribution due to shear and bending to the total transverse displacement are clarified. Using the extended Hamilton’s principle and defining an Airy stress function corresponding to the compatibility equation, the equations of motion, which do not explicitly include the in-plane displacements, are derived. The accuracy and effectiveness of the current model is shown by comparing the natural frequencies and buckling loads of various FG rectangular plates calculated by the proposed approach with even three-dimensional (3-D) and quasi-3D solutions. Besides, the exact dynamic response of a square FG plate due to a harmonic central force is investigated using modal analysis. This approach is capable of handling quasi-3D models , by selecting proper functions in the displacement field to consider the thickness stretching effect. By doing this, behavior of FG square plates with various coefficient functions are compared with each other. Therefore, through implementing the Airy stress function, the number of variables is reduced, in turn, simplifying the dynamic model. Consequently, it can be used for wide range study of static and dynamic behaviors of FG plates.
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.
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