Vibration of functionally graded shear and normal deformable porous microplates via finite element method

The size dependent natural frequencies of functionally graded (FG) shear and normal deformable porous square microplates are investigated within this paper for arbitrary boundary conditions. By utilizing the modified couple stress theory, the finite element model is developed based on a shear and normal deformation plate theory and the variational formulation. The material length scale parameter (MLSP) is taken as variable. The effects of the aspect ratio, gradient index, boundary condition, thickness to MLSP ratio, porosity volume fraction and variable MLSP on the dimensionless natural frequencies are investigated for the FG shear and normal deformable porous square microplates. It is found that the difference between the numerical computations employing the constant and variable material length scale parameters is significant. In addition, it is found that with an increment in the aspect ratio, the effect of the MLSP on the natural frequencies increases, especially for the thick microplates. It can be concluded that for the thick microplates (length/thickness <= 10), the effect of the variable MLSP on the natural frequencies with respect to the changing of the thickness to MLSP is more emphasized than the effect obtained by the constant MLSP for all studied boundary conditions.