VIBRATION ANALYSIS OF PLATES BY THE PB-2 RAYLEIGH-RITZ METHOD - MIXED BOUNDARY-CONDITIONS, REENTRANT CORNERS, AND INTERNAL CURVED SUPPORTS

This paper presents an efficient and accurate pb-2 Rayleigh-Ritz method for vibration analysis of elastic thin plates with arbitrary shape and boundary conditions. By using a Ritz function that consists of the product of a two-dimensional polynomial and a basic function that is the product of the boundary equations raised to the power of either 0, 1, or 2 for a free, simply supported, or clamped edge, respectively, the kinematic boundary conditions are automatically satisfied. Although this pb-2 Ritz function works for a large class of plate shapes, it encounters problems when (a) the boundary equations of simple and clamped supports pass through the plate domain, (b) the boundary conditions are mixed along the same edge, or (c) the internal curved supports do not span the plate. The paper presents a way to overcome these difficulties of the pb-2 Rayleigh-Ritz method by simulating the boundary conditions concerned, with a series of supporting points. As a result, the pb-2 Rayleigh-Ritz method can be applied to analysis of an even larger class of plate shapes and boundary conditions.