Flexural Vibration of In-Plane Loaded Plates with Straight Line/Curved Internal Supports

Abstract

An investigation into the vibration analysis of a class of in-plane loaded rectangular plates with internal supports of arbitrary contour is conducted. Solutions to this vibration problem are obtained based on the pb-2 Rayleigh-Ritz method. The Ritz function for this method is defined as the product of (1) a two-dimensional polynomial function expanded in a new manner, (2) equations of the internal support and (3) equations of the boundary supports each raised to the power of either 0, 1, or 2 corresponding to a free, simply supported or clamped edge, respectively. A comparison study on the convergence between the proposed set of polynomials and mathematically complete set of polynomials is conducted. The simplicity and accuracy of the method are demonstrated by analyzing square plates with either two intersecting internal line supports or a central ring support. The influence of the in-plane loads on the natural frequencies will be studied. Note that this paper presents some first known solutions to in-plane loaded rectangular plates with internal supports of arbitrary contour. The mode shapes for these plates are also presented in contour plots.