Accurate Results by the Ritz Method for Free Vibration of Uniform Annular Plates

Abstract

This paper describes an approach extended from Ritz method to analyze the free vibration of thin isotropic annular plates in good accuracy, and presents comprehensive lists of natural frequencies of the plate for all possible sets of classical boundary conditions. Analytical process is developed to introduce the boundary index that allows to accommodate any sets of free, simple supported and clamped edges along inner and outer boundary of the plate. Convergence and comparison studies are made to demonstrate numerical accuracy in the frequency parameters. Results are summarized for nine sets of boundary conditions and six different ratios of (inner radius)/(outer radius), and are intended to serve for uses of design data and comparison in relevant future papers.