Semi-analytical solution for free vibration of thick functionally graded plates rested on elastic foundation with elastically restrained edge

This paper deals with free vibration analysis of functionally graded thick circular plates resting on the Pasternak elastic foundation with edges elastically restrained against translation and rotation. Governing equations are obtained based on the first order shear deformation theory (FSDT) with the assumption that the mechanical properties of plate materials vary continuously in the thickness direction. A semi-analytical approach named differential transform method is adopted to transform the differential governing equations into algebraic recurrence equations. And eigenvalue equation for free vibration analysis is solved for arbitrary boundary conditions. Comparison between the obtained results and the results from analytical method confirms an excellent accuracy of the present approach. Afterwards, comprehensive studies on the FG plates rested on elastic foundation are presented. The effects of parameters, such as thickness-to-radius, material distribution, foundation stiffness parameters, different combinations of constraints at edges on the frequency, mode shape and modal stress are also investigated.