Free vibration of cracked FGM plates with variable thickness resting on elastic foundations

Abstract

Abstract In this paper, Shi s high-order shear deformation theory (HSDT) is introduced to compute the free vibration of the cracked functionally graded material (FGM) plates according to the power law resting on Pasternak elastic foundations. The rectangular plate has a linearly variable thickness and has a crack in the center. The phase field theory and finite element method are used to study the vibration frequency of plates depending on the exponent of the material as well as the parameters of the elastic foundation. Several numerical results have been compared with the ones available in the literature. Next, the paper investigates the effect of length, angle of crack, ratio of plate thickness to the free vibration of plates.