Three-dimensional vibration analyses of functionally graded plates under various boundary conditions

Abstract

Three-dimensional vibration solutions are presented for rectangular functionally graded plates with different boundary conditions, based on the small strain linear elasticity theory. The material properties are assumed to vary as a power form of the thickness coordinate. The Ritz method with Chebyshev displacement functions is used to solve the vibration problem of functionally graded plates. The convergence and comparison studies demonstrate the accuracy and correctness of the present method. The effects of aspect and thickness ratios, and gradient index, on the free vibration frequencies are investigated. Some results are given in the form of tables and figures, which can serve as the benchmark for further research.