Thermo-viscoelastic analysis of high-frequency motions of thin plates
type: Item
instance of: scholarly article
title: Thermo-viscoelastic analysis of high-frequency motions of thin plates
zbMATH Open document ID: 1001.74053
DOI: 10.1007/BF01250020
published in: Acta Mechanica
publication date: 2002-12-15T00:00:00Z
review text: Using the three-dimensional thermo-viscoelastodynamics, the authors derive a hierarchic system of two-dimensional equations in invariant differential and variational forms for the analysis of high-frequency motions of thin plates. First, a differential type of variational principles is presented in terms of Laplace-transformed field variables for fundamental equations of linear, non-isothermal, non-polar and non-local three-dimensional theory. Next a generalized versions of Mindlin's hypothesis for elastic plates is introduced for displacement and temperature fields. Then the hierarchic system of plate equations is systematically derived by means of the differential variational principle. The hierarchic system of two-dimensional equations governs the extensional, thickness-shear, flexural and torsional as well as coupled motions of thermoviscoelastic thin plates of uniform thickness at both low and high frequencies. Finally, the authors study certain cases involving special geometry, motions and materials, and investigate the uniqueness of solutions of the hierarchic system of plate equations.
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74D05
Mathematics Subject Classification ID: 74F05
zbMATH DE Number: 1506072
zbMATH Keywords: Laplace transform
zbMATH Keywords: three-dimensional thermo-viscoelastodynamics
zbMATH Keywords: thin plates
zbMATH Keywords: fundamental equations
zbMATH Keywords: Mindlin's hypothesis
zbMATH Keywords: hierarchic system of plate equations
zbMATH Keywords: differential variational principle
zbMATH Keywords: uniqueness
author: G. Aşkar Altay
author: M. Cengiz Dökmeci
reviewed by: Girish Kumar Ramaiah
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01250020
OpenAlex ID: W1972108905
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description: scientific article; zbMATH DE number 1506072