Sigmoid functionally graded plates embedded on Winkler-Pasternak foundation: Free vibration analysis by dynamic stiffness method

Abstract

In this present paper, the dynamic stiffness method has been formulated to calculate the natural frequency of sigmoid functionally graded material (S-FGM) plate embedded on the Winkler-Pasternak elastic foundation. The material properties of S-FGM continuously vary along the transverse direction of the plate by using two power-law variations in terms of volume fraction of the constituent's material. Hamilton's principle is implemented to derive the governing partial differential equation of motion based on the classical plate theory considering the physical neutral surf ace of the FGM rectangular plate. The Wittrick -Williams algorithm is applied as a solution technique to solve the transcendental nature of the dynamic stiffness matrix and extract the natural frequencies of the FGM plate with the desired accuracy. The S-FGM plate parameters’ variation of natural frequencies with the change of parametric numerical values (aspect ratio, sigmoid volume fraction index, boundary conditions and elastic foundation parameters, density ratio, and modulus ratio) are also highlighted. The DSM results are compared and validated with the available published literature. A new set of natural frequency results for the S-FGM plate embedded on the Winkler-Pasternak elastic foundation are generated.