Free vibration analysis of bi-directional functionally graded annular plates using finite annular prism methods

Based on Reissner's mixed variational theorem, the authors develop a finite annular prism method (FAPM) for the three-dimensional (3D) free vibration analysis of bi-directional functionally graded (FG) annular plates with assorted boundary conditions. In this formulation, the FG annular plate is divided into a number of finite annular prisms with triangular cross-sections, in which Fourier functions and Lagrange polynomials are used to interpolate the circumferential direction and radial-thickness surface variations of primary field variables in each individual prism, respectively. The material properties of the FG annular plate are assumed to obey an exponential function distribution varying doubly exponentially through the radial-thickness surface. These FAPM solutions for the frequency parameters and their corresponding mode shapes of the FG annular plate closely agree with the solutions obtained using other 3D approaches available in the literature.