A refined integral parabolic plate theory incorporating stretching effects for free vibration analysis of advanced composite plates on Winkler-Pasternak foundation

This paper presents a novel parabolic shear deformation plate theory including the stretching effect for free vibration of the simply supported functionally graded plates embedded on the Winkler-Pasternak elastic foundation. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. This theory has only five unknowns, which is even less than the other shear and normal deformation theories. The present one has a new displacement field which introduces undetermined integral variables. Material properties are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume power laws of the constituents. The equation of motion of the vibrated plate obtained via the classical Hamilton's principle and solved using Navier's steps. The accuracy of the proposed solution is checked by comparing the present results with those available in existing literature. The effects of the volume fraction index of functionally graded material, side-to-thickness ratio and Winkler-Pasternak elastic foundation on free vibration responses of the functionally graded plates are investigated. It can be concluded that the present theory is not only accurate but also simple in predicting the natural frequencies of functionally graded plates with stretching effect on elastic foundation.