Free vibration of bi-directional functionally graded sandwich plates using layerwise finite element approach

In this paper, layerwise finite element analysis for the free vibration behavior of two-dimensional functionally graded sandwich plates with different boundary conditions is presented. The plates consist of three layers; a functionally graded layer embedded between ceramic and metal isotropic layers. The layerwise approach is based on the third order shear deformation theory for the middle layer, while the first order shear deformation theory is used to model both the upper and lower isotropic layers. Quadrilateral 8-noded element with 13-degrees of freedom per node is used for this purpose. The present results show very good agreements with the published analytical results of plates consist of a single functionally graded layer. Furthermore, for sandwich plates good agreements were obtained when the present results are compared with similar problems solved by other methods in literature. Parametric studies were investigated for various plate parameters including applied boundary conditions, volume fraction exponents and plate side to thickness ratio.