Vibration response of exponentially graded plates on elastic foundation using higher-order shear deformation theory

Abstract

A non-polynomial hyperbolic based theory has been presented for the free vibration response of a rectangular plate with linearly varying thickness, which rests on an elastic foundation. Ceramic/ metal has considered as Functionally Graded Material (FGM) of the plate using exponential law for material gradation of properties in the thickness direction. The influence of Winkler’s and Pasternak's paremeter of foundation on the plate is investigated in conjunction with taper ratio. The governing equation of plates has established using the variational principle. Galerkin's technique has been followed for the solution of the eigen value problem of the presented model. The obtained results have compared with the observations of the isotropic tapered plate, and FGM plate for uniform thickness. The numerical result depicts the good accuracy of the present theory comparable to the existing shear deformation theory. The influences of thickness variation for a plate, has assumed to be simply supported and clamped, have investigated with various span ratio, aspect ratio, taper ratio and foundation stiffness.