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Journal ArticleDOI

One-dimensional problem of a fractional order two-temperature generalized thermo-piezoelasticity

01 Aug 2014-Mathematics and Mechanics of Solids (SAGE Publications)-Vol. 19, Iss: 6, pp 672-693
TL;DR: In this article, the authors derived the thermoelastic stress, strain and conductive temperature in a piezoelastic half-space body in which the boundary is stress free and subjected to thermal loading in the context of the fractional order generalized thermelasticity theory (2TT).
Abstract: This paper is concerned with the determination of the thermoelastic stress, strain and conductive temperature in a piezoelastic half-space body in which the boundary is stress free and subjected to thermal loading in the context of the fractional order two-temperature generalized thermoelasticity theory (2TT). The two-temperature three-phase-lag (2T3P) model, two-temperature Green–Naghdi model III (2TGNIII) and two-temperature Lord–Shulman (2TLS) model of thermoelasticity are combined into a unified formulation introducing unified parameters. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain that is then solved by the state-space approach. The numerical inversion of the transform is carried out by a method based on Fourier series expansion techniques. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. The effect of the fractional order parameter, two-temperature and electric field on...
Citations
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Journal ArticleDOI
TL;DR: In this article, a new model of magneto-thermoelasticity theory has been constructed in the context of a new consideration of heat conduction with memory-dependent derivative.
Abstract: In this work, a new model of magneto-thermoelasticity theory has been constructed in the context of a new consideration of heat conduction with memory-dependent derivative. One-dimensional application for a perfect electrically conducting half-space of elastic material, which is thermally shocked, in the presence of a constant magnetic field has been solved by using Laplace transform technique. According to the numerical results and its graphs, conclusion about the new theory of magneto-thermoelasticity has been constructed and compared with dynamic classical coupled theory.

68 citations

Journal ArticleDOI
TL;DR: In this paper, an ultrafast fractional magneto-thermoelasticity model utilizing the modified hyperbolic heat conduction model with fractional order is formulated to describe the thermo-elastic behavior of a thin perfect conducting metal film irradiated by a femtosecond laser pulse.
Abstract: An ultrafast fractional magneto-thermoelasticity model utilizing the modified hyperbolic heat conduction model with fractional order is formulated to describe the thermoelastic behavior of a thin perfect conducting metal film irradiated by a femtosecond laser pulse. Some theorems of generalized thermoelasticity follow as limit cases. The temporal profile of the ultrafast laser was regarded as being non-Gaussian. An analytical–numerical technique based on the Laplace transform was used to solve the governing equations and the time histories of the temperature, displacement, stress, strain, and induced electric/magnetic fields in a gold film were analyzed. Some comparisons have been shown in figures to estimate the effects of some parameters on all the studied fields.

43 citations


Cites methods from "One-dimensional problem of a fracti..."

  • ...Recently, the determination of the thermoelastic stress, strain and conductive temperature in a piezoelastic half-space body in the context of the fractional order two-emperature generalized thermoelasticity theory are obtained by Kanoria and Islam [16]....

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Journal ArticleDOI
TL;DR: In this paper, the authors presented a refined multi-phase-lags theory for a half-space medium with the inclusion of gravity, where the wave propagation of a gravitated piezo-thermoelastic half-spa...
Abstract: This work presents a refined multi-phase-lags theory for thermoelastic response of half-space medium with the inclusion of gravity. The wave propagation of a gravitated piezo-thermoelastic half-spa...

25 citations

Journal ArticleDOI
TL;DR: In this article, the authors investigated the transient phenomena in a homogeneous isotropic three-dimensional medium whose surface is subjected to a time-dependent thermal loading and is free of traction, in the context of two-temperature three-phase-lag thermoelastic model with non-local fractional operators.

22 citations

References
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Journal ArticleDOI
TL;DR: In this article, the integrodifferential equation (IDE) is decomposed by its decomposition for every α, 1≤α≤2 and α = 2.
Abstract: We are concerned with the integrodifferential equation (IDE)α: u(t, x)=O(x)+tα /2 /Γ(1+α/2)ψ(x)+1/Γ(α)∫ o t (t-s)α -1 Δu(s, x)ds for 1≤α≤2 Here Γ(x) is the gamma fonction and Δ=(∂/∂x) 2 When ψ=0, (IDE) 1 is reduced to the heat equation For α=2, (IDE) 2 is just the wave equation The aim of the present paper is to investigate the structure of the solution of (IDE)α by its decomposition for every α, 1≤α≤2

215 citations

Journal ArticleDOI
TL;DR: In this article, the authors considered two cases in the theory of the heat conduction models with three-phase-lag and proposed a suitable Lyapunov function for each one.

207 citations


"One-dimensional problem of a fracti..." refers background in this paper

  • ...Quintanilla and Racke [32] studied the stability of solutions in 3P heat conduction....

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Journal ArticleDOI
TL;DR: Within the framework of a linear two-temperature theory two separate wave propagation problems are investigated in this article, where interest is directed to wave speeds, travelling discontinuities in the two temperatures and the strain, and long and short time approximations.
Abstract: Within the framework of a linear two-temperature theory two separate wave propagation problems are investigated. Interest is directed to wave speeds, travelling discontinuities in the two temperatures and the strain, and long and short time approximations.

205 citations


"One-dimensional problem of a fracti..." refers background in this paper

  • ...Warren and Chen [6] have investigated wave propagation in the two-temperature theory of thermoelasticity....

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  • ...Chen and Gurtin [3] and Chen et al. [4, 5] have formulated a theory of heat conduction in deformable bodies, which depends on two distinct temperatures – the conductive temperature φ and the thermodynamic temperature θ ....

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Journal ArticleDOI
TL;DR: In this article, a theory of thermoelasticity for piezoelectric materials, including heat-flux among the independent constitutive variables, is formulated, and it is found that the linearized version of the theory admits a finite speed for thermal signals.
Abstract: A theory of thermoelasticity for piezoelectric materials which includes heat-flux among the independent constitutive variables is formulated. It is found that the linearized version of the theory admits a finite speed for thermal signals. An equation of energy balance and a theorem on the uniqueness of solution are obtained.

200 citations

Journal ArticleDOI
TL;DR: In this article, a complete set of axioms, based upon physically acceptable gross forms of the laws of thermodynamics, which yield appropriate forms of these laws for continuum physics; and find conditions under which these reduce to the classical forms.
Abstract: : The report presents a complete set of axioms, based upon physically acceptable gross forms of the laws of thermodynamics, which yield appropriate forms of these laws for continuum physics; and find conditions under which these reduce to the classical forms.

196 citations


"One-dimensional problem of a fracti..." refers background in this paper

  • ...Introduction Gurtin and Williams [1, 2] have suggested that there are no a priori grounds for assuming that the second law of thermodynamics for continuous bodies involves only a single temperature, i....

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  • ...Gurtin and Williams [1, 2] have suggested that there are no a priori grounds for assuming that the second law of thermodynamics for continuous bodies involves only a single temperature, i.e. it is more logical to assume a second law in which the entropy contribution due to heat conduction is governed by one temperature, that of the heat supply by another....

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