Abstract
A new shear deformation theory is introduced to conduct free vibration analysis of the functionally graded plates with simply supported boundary conditions. The shear functions presented in this study vary with gradient index and satisfy the stress-free boundary conditions on the top and bottom surfaces of functionally graded plates without using any shear correction factor. The displacement field is expressed as undetermined integral terms. The governing differential equation and boundary conditions are derived based on Hamilton's principle. The material properties of the functionally graded plates discussed in this paper are assumed to vary through the thickness according to the power-law distribution and the Mori-Tanaka scheme. The amplitude-frequency relationships of the FGM plates are presented and compared with the exsiting results and the obtained numerical results are compared with other 2D and quasi-3D solutions to verify the accuracy and efficiency of the present theory.
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