Three-dimensional vibration analysis of functionally graded thick, annular plates with variable thickness via polynomial-Ritz method

Abstract

In this paper, free vibration analysis of functionally graded thick, annular plates with linear and nonlinear thickness variation along the radial direction is investigated by using the polynomial-Ritz method. The material properties of the functionally graded plates are assumed to be graded in the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents. The solution procedure is based on the linear, small strain, three-dimensional elasticity theory. Potential (strain) and kinetic energies of the plates are formulated, and the polynomial-Ritz method is used to solve the eigenvalue problem. In this analysis method, a set of orthogonal polynomial series for three displacement components in a cylindrical polar coordinate are used to extract an eigenvalue equation yielding natural frequencies. Upper bound convergence of the non-dimensional frequencies to the exact values within at least four significant digits is demonstrated. Numerical results are presented and compared with the available literature. The vibration frequencies are given in several examples for various boundary conditions for the first time.