Effect of porosity distribution rate for the analysis of free vibrations of imperfect functionally graded plates

The vibrational behavior of simply supported imperfect functionally graded plates is studied and analyzed in this paper, and different types of porosity distribution rate is considered. Using higher-order shear deformation theory, This new model meets the nullity of the transverse shear stress at the upper and lower surfaces of the plate,transverse shear effects are studied as a function of plate thickness. Without the application of a shear correction coefficient, the current model contains only four unknowns. The mechanical properties of the plates are assumed to vary through the thickness according to a power law distribution in terms of the volume fractions of the constituents. Hamilton's principle is used to obtain the equations of motion. The closed form solutions are derived by using Navier’s method and then fundamental frequencies are obtained by solving the results of eigenvalue problems. the results of this analysis are presented and compared with those available in the literature.