Natural frequencies of shear deformable rhombic plates with clamped and simply supported edges
type: Item
instance of: scholarly article
title: Natural frequencies of shear deformable rhombic plates with clamped and simply supported edges
zbMATH Open document ID: 0823.73036
DOI: 10.1016/0020-7403(94)90064-7
author: Yanyan Li
published in: International Journal of Mechanical Sciences
publication date: 1995-10-30T00:00:00Z
review text: The natural vibrations of thick and thin rhombic plates with clamped and simply supported edges are analyzed, using assemblages of nine-node Lagrangian isoparametric quadrilateral \(C^ 0\) continuous finite elements, and using a higher-order shear deformable thick plate theory. Here, additional nodal displacement degrees of freedom are derived by retaining higher-order powers of the thickness coordinate in the in-plane displacement fields, wihch in turn allows for the proper representation of the transverse shear strains of thick plates. Essential rotary inertia terms are derived and included in the present analysis. Nondimensional frequencies are calculated for thick and thin rhombic plates having various combinations of clamped and simply supported edge conditions, and skew angles. The efficacy of using higher-order shear deformable plate finite elements for predicting the in-plane vibration modes of rhombic plates is found to increase as the span-to-thickness ratio decreases and the skew angle increases. The work shows that higher- order shear deformable finite elements essentially eliminate the transverse shear over-correction of thick rhombic plate frequencies, that is produced when finite elements based on the widely used first-order Reissner-Mindlin plate theory are used.
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74S05
zbMATH DE Number: 755003
zbMATH Keywords: nine-node Lagrangian isoparametric quadrilateral elements
zbMATH Keywords: higher-order shear deformable thick plate theory
zbMATH Keywords: rotary inertia terms
zbMATH Keywords: span-to- thickness ratio
reviewed by: Girish Kumar Ramaiah
MaRDI profile type: Publication
full work available at URL: 0020-7403(94)90064-7
OpenAlex ID: W2084029627
description: scientific article; zbMATH DE number 755003