Analytical solution for free vibration analysis of plates functionally graded FGP with porosities

In this paper, an analytical solution for the analysis of the free vibration of plates in functionally graded material (FGM) is presented, considering the porosities that can occur inside the materials with gradient properties (FGM) during of their manufacture. A method based on high order theory will be presented to study the free vibration of FGM plates. The proposed theory contains four unknowns unlike other theories. The governing equations are obtained through the Hamilton’s principal and the closed form solutions in terms of natural frequencies are obtained by using Navier technique. The numerical results obtained through the present analysis are compared with the ones available in the literature. The effects of various parameters, such as thickness ratio, gradient index, and porosity factor on the free vibration of FGM plates are all discussed