Natural frequencies of rectangular plates
type: Item
instance of: scholarly article
title: Natural frequencies of rectangular plates
zbMATH Open document ID: 0885.73031
DOI: 10.1016/S0093-6413(96)00068-7
published in: Mechanics Research Communications
publication date: 1998-05-03T00:00:00Z
review text: In the absence of point supports at the corner of rectangular plates where two free edges meet, 21 combinations of boundary conditions arise, with additional 12 cases occurring if point supports at corners are included. In this note, a formulation treating these 33 cases in a unified manner is presented. The formulation is variationally based, which leads to symmetrical matrices, and enables a modified form of the sign counting algorithm to be employed. The governing differential equation is satisfied within the plate, reducing the two-dimensional problem to the determination of unknown coefficients defining boundary displacement and normal moments. With thin plate theory, two boundary conditions must be satisfied on any boundary. In the proposed method, transverse displacement and normal moment boundary conditions are satisfied exactly, while normal rotation and Kirchhoff shear boundary conditions are satisfied in an integral sense as a consequence of the variational procedure. It is observed that with all combinations of boundary conditions occurring with single plates, the two normal moments at plate corners are zero. This condition is satisfied exactly in the method described in this note.
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74P10
zbMATH DE Number: 1077148
zbMATH Keywords: sign counting algorithm
zbMATH Keywords: boundary displacement
zbMATH Keywords: normal moments
zbMATH Keywords: thin plate theory
zbMATH Keywords: Kirchhoff shear boundary conditions
zbMATH Keywords: variational procedure
author: B. W. Golley
MaRDI profile type: Publication
full work available at URL: s0093-6413(96)00068-7
OpenAlex ID: W2061261056
description: scientific article; zbMATH DE number 1077148