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

doi:10.1177/1081286513482605

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

Journal Article•DOI•

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

Mohsin Islam¹, Mridula Kanoria²•Institutions (2)

St. Xavier's College-Autonomous, Mumbai¹, University of Calcutta²

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).

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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...

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Journal Article•DOI•

A novel magneto-thermoelasticity theory with memory-dependent derivative

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Magdy A. Ezzat¹, Ahmed S. El-Karamany², Alaa A. El-Bary•Institutions (2)

Alexandria University¹, University of Nizwa²

23 Apr 2015-Journal of Electromagnetic Waves and Applications

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.

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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.

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68 citations

INTEGRODIFFERENTIAL EQUATION WHICH INTERPOLATES THE HEAT EQUATION AND THE WAVE EQUATION II(Martingales and Related Topics)

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安啓藤田

01 Nov 1989

47 citations

Journal Article•DOI•

Fractional ultrafast laser-induced magneto-thermoelastic behavior in perfect conducting metal films

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Magdy A. Ezzat¹, Ahmed S. El-Karamany², Alaa A. El-Bary, Mohsen A. Fayik¹•Institutions (2)

Alexandria University¹, University of Nizwa²

02 Jan 2014-Journal of Electromagnetic Waves and Applications

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.

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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.

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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 Article•DOI•

Wave propagation of a gravitated piezo-thermoelastic half-space via a refined multi-phase-lags theory

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Ashraf M. Zenkour¹, Ashraf M. Zenkour²•Institutions (2)

Kafrelsheikh University¹, King Abdulaziz University²

16 Nov 2020-Mechanics of Advanced Materials and Structures

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...

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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...

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25 citations

Journal Article•DOI•

Thermo-viscoelastic Interaction in a Three-dimensional Problem Subjected to Fractional Heat Conduction

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Sayak Chakravorty¹, Suman Ghosh¹, Abhik Sur²•Institutions (2)

Techno India¹, University of Calcutta²

01 Jan 2017-Procedia Engineering

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.

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22 citations

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Journal Article•DOI•

Generalized thermoelastic functionally graded orthotropic hollow sphere under thermal shock with three-phase-lag effect

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Avijit Kar¹, Mridula Kanoria²•Institutions (2)

St. Xavier's College-Autonomous, Mumbai¹, University of Calcutta²

01 Jul 2009-European Journal of Mechanics A-solids

TL;DR: In this article, the Laplace transformation has been applied to the problem of determining the thermo-elastic interaction due to step input of temperature on the boundaries of a functionally graded orthotropic hollow sphere in the context of linear theories of generalized thermoelasticity.

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Abstract: This problem deals with the determination of thermo-elastic interaction due to step input of temperature on the boundaries of a functionally graded orthotropic hollow sphere in the context of linear theories of generalized thermo-elasticity. Using the Laplace transformation the fundamental equations have been expressed in the form of vector–matrix differential equation which is then solved by eigenvalue approach. The inverse of the transformed solution is carried out by applying a method of Bellman et al. Stresses, displacement and temperature distributions have been computed numerically and presented graphically in a number of figures. A comparison of the results for different theories (TEWOED(GN-II), TEWED(GN-III) and three-phase-lag model) is presented. When the material is homogeneous, isotropic and outer radius of the hollow sphere tends to infinity, the corresponding results agree with that of existing literature for GN-III model.

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93 citations

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

...Kanoria and Mallik [35] studied generalized thermoviscoelastic interaction in an infinite Kelvin–Voigt solid due to periodically varying heat source with the 3P effect....
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...Fractional order two-temperature generalized thermoelasticity with finite wave speed was investigated by Sur and Kanoria [77]....
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...Islam and Kanoria [37] have investigated 3P effects in a two-dimensional transversely isotropic thick plate....
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...Kar and Kanoria [34] studied the thermoviscoelastic stresses in an isotropic viscothermoelastic homogeneous spherical shell due to step input of temperature in the stress free boundaries of the shell in the context of TEWED and 3P models of generalized thermoelasticity....
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...Banik and Kanoria [54, 55] studied two-temperature generalized thermoelastic interactions in an infinite body with a spherical cavity....
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Journal Article•DOI•

Fractional order theory of a perfect conducting thermoelastic medium

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Magdy A. Ezzat¹, Magdy A. Ezzat², Ahmed S. El-Karamany¹, Ahmed S. El-Karamany²•Institutions (2)

Alexandria University¹, University of Nizwa²

15 Mar 2011-Canadian Journal of Physics

TL;DR: In this paper, a new mathematical model of magneto-thermoelasticity theory is constructed in the context of a new consideration of heat conduction law with time-fractional order.

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Abstract: In this work, a new mathematical model of magneto-thermoelasticity theory is constructed in the context of a new consideration of heat conduction law with time-fractional order. This model is appli...

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93 citations

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

...Ezzat et al. [76] have also investigated the fractional order theory with the 3P effect....
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...∂ξ qi ∂tξ = −k∇T , 0 ξ ≤ 1 (10) El-Karamany and Ezzat [73] introduced two general models of fractional heat conduction law for a nonhomogeneous anisotropic elastic solid....
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...For fractional thermoelasticity not involving two temperatures, El-Karamany and Ezzat [74] established the uniqueness, reciprocal theorems and convolution variational principle....
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...Fractional order theory of a perfect conducting thermoelastic medium not involving two temperatures was investigated by El-Karamany and Ezzat [75]....
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...Ezzat established a new model of a fractional heat conduction equation by using the new Taylor series expansion of time-fractional order, developed by Jumarie [72] as qi + τ ξ 0 ξ !...
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Journal Article•DOI•

Fractional order theory in thermoelastic solid with three-phase lag heat transfer

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Magdy A. Ezzat¹, Magdy A. Ezzat², Ahmed S. El Karamany³, Mohsen A. Fayik²•Institutions (3)

Qassim University¹, Alexandria University², University of Nizwa³

01 Apr 2012-Archive of Applied Mechanics

TL;DR: In this article, the field equations of the linear theory of thermoelasticity have been constructed in the context of a new consideration of Fourier law of heat conduction with time-fractional order and three-phase lag.

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Abstract: In this work, the field equations of the linear theory of thermoelasticity have been constructed in the context of a new consideration of Fourier law of heat conduction with time-fractional order and three-phase lag. A uniqueness and reciprocity theorems are proved. One-dimensional application for a half-space of elastic material in the presence of heat sources has been solved using Laplace transform and state space techniques Ezzat (Canad J Phys Rev 86:1241–1250, 2008). According to the numerical results and its graphs, conclusion about the new theory has been established.

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80 citations

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

...[76] have also investigated the fractional order theory with the 3P effect....
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Journal Article•DOI•

On the linear coupled thermoelasticity with two temperatures

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Dorin Ieşan

01 Jul 1970-Zeitschrift für Angewandte Mathematik und Physik

TL;DR: In this article, the lineare Theorie der Thermoelastizitat zweier verschiedener Temperaturen is betrachtet, werden ein Eindeutigkeitssatz, Reziprozitatssatze und ein Variationssatz bewiesen.

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Abstract: In dieser Arbeit wird die lineare Theorie der Thermoelastizitat zweier verschiedener Temperaturen betrachtet. Es werden ein Eindeutigkeitssatz, Reziprozitatssatze und ein Variationssatz bewiesen.

...read moreread less

78 citations

Journal Article•DOI•

Generalized thermo-piezoelectric problems with temperature-dependent properties

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Moncef Aouadi

01 Oct 2006-International Journal of Solids and Structures

TL;DR: The model of generalized thermo-piezoelectricity in an isotropic elastic medium with temperature-dependent mechanical properties is established in this paper, where the modulus of elasticity is taken as a linear function of reference temperature.

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75 citations