The free vibration of non-rotating and rotating multi-directional functionally graded annular plates are studied in this thesis. The concept of functionally graded materials was first introduced in 1984 as ultrahigh-temperature-resistant materials for aircrafts, space vehicles and other engineering applications. The functionally graded materials are composite materials that are microscopically inhomogeneous, and their mechanical properties vary continuously in one or more directions. Non-rotating and rotating annular plates are used in many engineering applications, so that using the functionally graded materials in these structures is useful. The vibration analysis of circular and annular plates are presented in two parts, non-rotating and rotating. First, the three-dimensional free vibration of non-rotating multi-directional functionally graded plates is studied. The three-dimensional elasticity theory is used to analyze the free vibration of the plate. It is assumed that the material properties vary in both thickness and radial directions, so that the plate is made of bi-directional functionally graded material. The governing equations are solved by a semi-analytical numerical method which is the state space based differential quadrature method. This method solves the problem analytically in thickness direction by the state space method and useing the differential quadrature method to solve the problem in radial direction numerically. The accuracy and convergence of method are studied and the natural frequencies of these plates are determined for different kind of functionally graded materials and different type of boundary conditions is obtained. The influence of various parameters such as, inner radius-to-outer radius ratio, thickness-to-outer radios ratio and graded indices on natural frequencies are demonstrated. It is shown that the increase of inner radius-to-outer radius ratio and thickness-to-outer radios ratio increase the natural frequencies of non-rotating functionally graded plates. The effects of graded indices on natural frequencies are different. The increase of the absolute value of thickness graded index, decreases the natural frequencies and the variations of radial graded index have different effects on natural frequencies of plates with different kind of boundary conditions. The corresponding displacements mode shapes are drawn. In the second part, the free vibration analysis of rotating functionally graded annular plates is discussed. Key Words: Free Vibration, Annular Plate, Functionally Graded Material, Differential Quadrature Method.
