Finite element analysis of free vibration of functionally graded porous circular plate reinforced with graphene

In this paper, the finite element analysis of the free vibrations of functionally graded porous circular plate reinforced with graphene based on the first order shear deformation theory (FSDT) is presented for the first time. The governing equations are obtained using Hamilton's principle and the finite element method (FEM) is used to solve the governing equations of the sheet. The results of the present work were compared with previous studies and a good agreement between the results was observed. The effect of different parameters such as porosity distribution, porosity coefficient, different GPL patterns and weight percentage of graphene nanoparticles, types of boundary conditions and also the ratio of thickness to radius on the vibrations of the circular sheet was investigated. Next, while validating the analysis method, the results obtained from the numerical solution were compared and analyzed. In the results, it was found that the effect of weight percentage of graphene and different types of graphene patterns as well as support conditions in sheet vibrations is more than other cases.