three dimensional free vibration of fgm circular plates using semi-analytical method

in this research three-dimensional free vibration analysis of functionally graded circular plate with various boundary conditions is achieved. 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. numerical results are given to demonstrate the accuracy and superiority of the presented method. the numerical results are compared with the existing numerical solutions and good agreement is displayed .using the semi-analytical method, the analytical solution in the thickness direction is given and an effective approximate solution in the radial direction is obtained by selecting fewer discrete points.