Analysis on free vibration and critical buckling load of a FGM porous rectangular plate

Abstract

The properties of functionally gradient materials (FGM) are closely related to porosity, which has effect on FGM's elastic modulus, Poisson's ratio, density, etc. Based on the classical theory of thin plates and Hamilton principle, the mathematical model of free vibration and buckling of FGM porous rectangular plates with compression on four sides is established. Then the dimensionless form of the governing differential equation is also obtained. The dimensionless governing differential equation and its boundary conditions are transformed by differential transformation method (DTM). After iterative convergence, the dimensionless natural frequencies and critical buckling loads of the FGM porous rectangular plate are obtained. The problem is reduced to the free vibration of FGM rectangular plate with zero porosity and compared with its exact solution. It is found that DTM gives high accuracy result. The validity of the method is verified in solving the free vibration and buckling problems of the porous FGM rectangular plates with compression on four sides. The results show that the elastic modulus of FGM porous rectangular plate decreases with the increase of gradient index and porosity. Furthermore, the effects of gradient index and porosity on dimensionless natural frequencies and critical buckling loads are further analyzed under different boundary conditions with constant aspect ratio, and the effects of aspect ratio and load on dimensionless natural frequencies under different boundary conditions.