Free axisymmetric vibrations of FGM circular plates

This work presents an approach named direct displacement method to investigate the free axisymmetric vibrations of transversely isotropic FGM circular plates whose material properties can be varied arbitrarily along the thickness of the plate. If the variation of the material properties obeys the exponential law, three-dimensionally exact solutions are obtained for two specific boundary conditions, which rigorously satisfy the governing equations and boundary conditions at every point. Alternatively, semi-analytical solutions are obtained for arbitrary variation of material properties. Numerical examples are finally shown to demonstrate the present method.