Flexural vibrations of rectangular plates with free edges
type: Item
instance of: scholarly article
title: Flexural vibrations of rectangular plates with free edges
zbMATH Open document ID: 0613.73054
DOI: 10.1016/0093-6413(86)90049-2
author: R. D. Mindlin
published in: Mechanics Research Communications
publication date: 1986-01-01T00:00:00Z
review text: In this paper, equations of flexural vibrations of isotropic, elastic plates, with rotatory inertia and shear deformation terms included, are solved for rectangular plates with all four edges free. The solutions are exact and in closed form. Two main restrictions apply: (1) the length/width ratio must be a ratio of integers; (2) for each value of Poisson's ratio, all the allowable modes must have the same frequency. In each case, that frequency lies between about 1.9 and 2.7 times the frequency, say \(\omega_ 0\), of the fundamental thickness-shear mode of the infinite plate. However, the equations, with the appropriate shear- correction factor, are intended for use at frequencies no higher than about \(1.2\omega_ 0\). To improve the accuracy at the higher frequencies, two additional correction factors are introduced to make the equations produce the exact values of frequency and wave-number, obtained from Rayleigh's exact dispersion relation, at the frequency and for the Poisson's ratio required by the solution for the rectangular plate.
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74K20
zbMATH DE Number: 3993033
zbMATH Keywords: flexural vibrations
zbMATH Keywords: isotropic, elastic plates
zbMATH Keywords: rotatory inertia
zbMATH Keywords: shear deformation
zbMATH Keywords: rectangular plates
zbMATH Keywords: all four edges free
zbMATH Keywords: exact
zbMATH Keywords: closed form
zbMATH Keywords: higher frequencies
zbMATH Keywords: two additional correction factors
MaRDI profile type: Publication
full work available at URL: 0093-6413(86)90049-2
OpenAlex ID: W2046894903
description: scientific article; zbMATH DE number 3993033