Fractional calculus in one-dimensional isotropic thermo-viscoelasticity

被引：55
|
作者：
Ezzat, Magdy A. [1 ]
El-Karamany, Ahmed S. [2 ]
El-Bary, Alaa A. [3 ]
Fayik, Mohsen A. [1 ]
机构：
[1] Univ Alexandria, Fac Educ, Dept Math, Alexandria, Egypt
[2] Nizwa Univ, Dept Math & Phys Sci, Nizwa 611, Oman
[3] Arab Acad Sci & Technol, Alexandria, Egypt
来源：
COMPTES RENDUS MECANIQUE | 2013年 / 341卷 / 07期
关键词：
Thermo-viscoelasticity; Fractional relaxation function; Non-Fourier heat conduction; State space approach; Laplace transforms; Fractional calculus; STATE-SPACE APPROACH; MAGNETO-THERMOELASTICITY; ORDER THEORY; FORMULATION; UNIQUENESS; THEOREMS;
D O I：
10.1016/j.crme.2013.04.001
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
A new fractional relaxation operator is derived using the methodology of fractional calculus. The governing coupled fractional differential equations in the frame of the thermo-viscoelasticity with fractional order heat transfer are applied to the one-dimensional problem with heat sources. Laplace transform and state space techniques are used to get the solution. According to the numerical results and its graphs, conclusion about the new theory of thermo-viscoelasticity has been constructed. The theories of coupled thermo-viscoelasticity and of generalized thermo-viscoelasticity with one relaxation time follow as limit cases. (C) 2013 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
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页码：553 / 566
页数：14
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