Semi-analytical solution for three-dimensional vibration of functionally graded circular plates

Based on the three-dimensional theory of elasticity and assuming that the mechanical properties of the materials vary continuously in the thickness direction and have the same exponent-law variations, the three-dimensional free and forced vibration analysis of functionally graded circular plate with various boundary conditions is achieved in this paper. A semi-analytical method, which makes use of the state space method and the one-dimensional differential quadrature method, is used to obtain the vibration frequencies and dynamic responses of circular plates. The analytical solution in the thickness direction can be acquired using the state space method and approximate solution in the radial direction can be obtained using the one-dimensional differential quadrature method. Numerical results are given to demonstrate the accuracy and superiority of the presented method. The influences of the material property graded index, the circumferential wave number and the forced frequencies on the dynamic behavior for different functionally graded circular plates are also studied.