Free vibration of advanced composite plates using a new higher order shear deformation theory

Abstract

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.