Vibration of porous functionally graded plates with geometric discontinuities and partial supports

Vibrational study of the porous functionally graded plate with geometric discontinuities and partial supports has been presented in the present paper. The kinematics of functionally graded plate is based on the refined exponential shear deformation theory. The displacement field has been refined by dividing the in-plane and out of the plane displacements into bending and shear components. The theory accounts for the nonlinear transverse shear stress variation along with the thickness with only four unknowns. The closed-form solution (Navier's solution), as well as FEM-based solution, have been used for the vibration analysis of functionally graded plate. The geometric discontinuities have been incorporated in terms of a circular cut-out of different sizes at the center of the plate. Modified rule of mixtures, modified sigmoid law, and trigonometric law have been used to compute the effective material properties of the functionally graded plate. A C-0 continuous iso-parametric FEM formulation has been used to attain the results in the case of FEM solution, and the efficacy of the present solution is demonstrated by comparing the results with the available literature. The results reflect that the porosity inclusion, circular cut-out, and position of the boundary constraints have a notable influence on the fundamental frequency of the functionally graded plate. It is also concluded that after a specific radius of circular cut-out, the vibration response of functionally graded plate exhibits nonlinearity in nature.