Thermodynamical Restrictions and Wave Propagation for a Class of Fractional Order Viscoelastic Rods

Thermodynamical Restrictions and Wave Propagation for a Class of Fractional Order Viscoelastic Rods

We discuss thermodynamical restrictions for a linear constitutive equation containing fractional derivatives of stress and strain of different orders. Such an equation generalizes several known models. The restrictions on coefficients are derived by using entropy inequality for isothermal processes....

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Main Authors: Teodor M. Atanacković, Sanja Konjik, Ljubica Oparnica, Dušan Zorica
Format: Article
Language:English
Published: Hindawi Limited 2011-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2011/975694
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spelling doaj-fc3df318967f479686ddffc580cf7e7b2020-11-25T02:25:20ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/975694975694Thermodynamical Restrictions and Wave Propagation for a Class of Fractional Order Viscoelastic RodsTeodor M. Atanacković0Sanja Konjik1Ljubica Oparnica2Dušan Zorica3Faculty of Technical Sciences, Institute of Mechanics, University of Novi Sad, Trg D. Obradovića 6, 21000 Novi Sad, SerbiaDepartment of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Trg D. Obradovića 4, 21000 Novi Sad, SerbiaFaculty of Education, University of Novi Sad, Podgorička 4, 25000 Sombor, SerbiaInstitute of Mathematics, SANU, Kneza Mihaila 35, 11000 Belgrade, SerbiaWe discuss thermodynamical restrictions for a linear constitutive equation containing fractional derivatives of stress and strain of different orders. Such an equation generalizes several known models. The restrictions on coefficients are derived by using entropy inequality for isothermal processes. In addition, we study waves in a rod of finite length modelled by a linear fractional constitutive equation. In particular, we examine stress relaxation and creep and compare results with the quasistatic analysis.http://dx.doi.org/10.1155/2011/975694
collection DOAJ
language English
format Article
sources DOAJ
author Teodor M. Atanacković
Sanja Konjik
Ljubica Oparnica
Dušan Zorica
spellingShingle Teodor M. Atanacković
Sanja Konjik
Ljubica Oparnica
Dušan Zorica
Thermodynamical Restrictions and Wave Propagation for a Class of Fractional Order Viscoelastic Rods
Abstract and Applied Analysis
author_facet Teodor M. Atanacković
Sanja Konjik
Ljubica Oparnica
Dušan Zorica
author_sort Teodor M. Atanacković
title Thermodynamical Restrictions and Wave Propagation for a Class of Fractional Order Viscoelastic Rods
title_short Thermodynamical Restrictions and Wave Propagation for a Class of Fractional Order Viscoelastic Rods
title_full Thermodynamical Restrictions and Wave Propagation for a Class of Fractional Order Viscoelastic Rods
title_fullStr Thermodynamical Restrictions and Wave Propagation for a Class of Fractional Order Viscoelastic Rods
title_full_unstemmed Thermodynamical Restrictions and Wave Propagation for a Class of Fractional Order Viscoelastic Rods
title_sort thermodynamical restrictions and wave propagation for a class of fractional order viscoelastic rods
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2011-01-01
description We discuss thermodynamical restrictions for a linear constitutive equation containing fractional derivatives of stress and strain of different orders. Such an equation generalizes several known models. The restrictions on coefficients are derived by using entropy inequality for isothermal processes. In addition, we study waves in a rod of finite length modelled by a linear fractional constitutive equation. In particular, we examine stress relaxation and creep and compare results with the quasistatic analysis.
url http://dx.doi.org/10.1155/2011/975694
work_keys_str_mv AT teodormatanackovic thermodynamicalrestrictionsandwavepropagationforaclassoffractionalorderviscoelasticrods
AT sanjakonjik thermodynamicalrestrictionsandwavepropagationforaclassoffractionalorderviscoelasticrods
AT ljubicaoparnica thermodynamicalrestrictionsandwavepropagationforaclassoffractionalorderviscoelasticrods
AT dusanzorica thermodynamicalrestrictionsandwavepropagationforaclassoffractionalorderviscoelasticrods
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