Refined 2-D theories for free vibration analysis of annular plates: Unified Ritz formulation and numerical assessment

This paper presents a unified Ritz-based method for the computation of modal properties of both thick and thin, circular and annular isotropic plates with different boundary conditions. The solution is based on an appropriate and simple formulation capable of handling in an unified way a large variety of two-dimensional higher-order plate theories. The formulation is also invariant with respect to the set of Ritz admissible functions. In this work, accurate upper-bound vibration solutions are presented by using kinematic models up to sixth order and products of Chebyshev polynomials and boundary-compliant functions. Considering the circumferential symmetry of annular plates and the 2-D nature of underlying theories, the present method is also computationally efficient since only single series of trial functions in the radial direction are required.