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•

Strange kinetics, porous media, and NMR

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Rainer Kimmich¹•Institutions (1)

University of Ulm¹

01 Nov 2002

TL;DR: In this article, the authors examined diffusion, hydrodynamic dispersion, flow, and thermal convection under the influence of geometrical confinements and surface interactions in porous media.

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Abstract: Nuclear magnetic resonance (NMR) techniques cover a broad range of length and time scales on which dynamic properties of fluids confined in porous media can be investigated. This report refers to field-cycling NMR relaxometry, field gradient NMR diffusometry and NMR microscopy. The objective was to examine diffusion, hydrodynamic dispersion, flow, and thermal convection under the influence of geometrical confinements and surface interactions in porous media. The anomalous character of these phenomena will be demonstrated and discussed in comparison with computer simulations and theoretical concepts. The first part of this presentation is devoted to nanoporous samples. It is shown that molecular Levy walks along inner surfaces occur under certain conditions. Mutual “obstruction” of molecules in molecular sieves and zeolites is another source of diffusion anomaly known as single-file diffusion which can be described by Gaussian propagators with a diffusion coefficient depending on time in a certain limit. In the case of polymers confined in narrow artificial tubes of a porous solid matrix, the characteristics of reptation were experimentally verified. The second part mainly refers to “trapping” effects as a source of anomalous transport characterised by non-Gaussian propagators. Model objects fabricated on the basis of percolation cluster models were examined with respect to flow, diffusion, thermal convection and hydrodynamic dispersion. The elucidation of transport laws in model systems of well defined and mathematically describable geometries is considered to be a promising way for the exploration of the structure/dynamics relationship in porous media as a long-term objective.

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186 citations

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

...According to Kimmich [65], equation (15) describes different cases of diffusion where 0 ξ 1 corresponds to weak diffusion (subdiffusion), ξ = 1 corresponds to normal diffusion, 1 ξ < 2 corresponds to strong diffusion (superdiffusion) and ξ = 2 corresponds to ballistic diffusion....
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...According to Kimmich [65], equation (15) describes different cases of diffusion where 0 < ξ < 1 corresponds to weak diffusion (subdiffusion), ξ = 1 corresponds to normal diffusion, 1 < ξ < 2 corresponds to strong diffusion (superdiffusion) and ξ = 2 corresponds to ballistic diffusion....
[...]
...Recently, considerable research effort has been expended to study anomalous diffusion, which is characterized by the time-fractional diffusion-wave equation by Kimmich [65] as follows ρc = κI c,ii (1)...
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...According to Kimmich [65], equation (1) describes different cases of diffusion where 0 ξ 1 corresponds to weak diffusion (subdiffusion), ξ = 1 corresponds to normal diffusion, 1 ξ 2 corresponds to strong diffusion (superdiffusion) and ξ = 2 corresponds to ballistic diffusion....
[...]
...Recently, considerable research effort has been expended to study anomalous diffusion, which is characterized by the time-fractional diffusion-wave equation by Kimmich [65] as follows ρc = κIξ c,ii (1) where ρ is the mass density, c the concentration, κ the diffusion conductivity, i the coordinate symbol, which takes the value 1, 2, 3....
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Journal Article•DOI•

Generalized thermoelasticity: closed-form solutions

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Richard B. Hetnarski¹, Józef Ignaczak¹•Institutions (1)

Rochester Institute of Technology¹

01 Oct 1993-Journal of Thermal Stresses

TL;DR: In this paper, a study of the one-dimensional thermoelastic wave produced by an instantaneous plane source of heat in homogeneous isotropic infinite and semi-infinite bodies of the Green-Lindsay (G-L) type is presented.

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Abstract: A study of the one-dimensional thermoelastic waves produced by an instantaneous plane source of heat in homogeneous isotropic infinite and semi-infinite bodies of the Green-Lindsay (G-L) type is presented. Closed-form Green's functions corresponding to the plane heat source are obtained using the decomposition theorem for a potential-temperature wave of the G-L theory. Qualitative analysis of the results is included.

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149 citations

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

...The third generalization to the coupled thermoelasticity theory is known as low-temperature thermoelasticity introduced by Hetnarski and Ignaczak [16], called HI theory....
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...Hetnarski and Ignaczak [11] examined five generalizations of the coupled theory of thermoelasticity....
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...Problems concerning generalized theories such as ETE and TRDTE have been studied by Chandrasekharaiah [14] and Ignaczak [15]....
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Journal Article•DOI•

State space afproach to thermoelasticity

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Leon Y. Bahar, Richard B. Hetnarski

01 Jul 1978-Journal of Thermal Stresses

TL;DR: In this paper, the matrix exponential method was applied to the non-dimensional equations of coupled thermoelasticity and the results obtained can be used to generate solutions in the Laplace transform domain to a broad class of problems in thermo-elasticy.

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Abstract: The method of the matrix exponential, which constitutes the basis of the state space approach of modern control theory, is applied to the nondimensional equations of coupled thermoelasticity. The disadvantages of using the thermoelastic potential are thus avoided. The results obtained can be used to generate solutions in the Laplace-transform domain to a broad class of problems in thermoelasticity. Applications to problems pertaining to a half-space and a layer are presented.

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147 citations

Book Chapter•DOI•

On the Equations of Motion of Piezoelectric Crystals

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Raymond D. Mindlin

01 Jan 1989

135 citations

Journal Article•DOI•

On the propagation of harmonic plane waves under the two-temperature theory

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Pratap Puri¹, P.M. Jordan²•Institutions (2)

University of New Orleans¹, United States Naval Research Laboratory²

01 Oct 2006-International Journal of Engineering Science

TL;DR: In this paper, the propagation of harmonic plane waves in media described by the two-temperature theory of thermoelasticity (2TT) is investigated, and exact dispersion relation solutions are determined and several characterizations of the wave field are examined.

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113 citations

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

...Email: k_mri@yahoo.com established uniqueness and reciprocity theorems for the 2TT. Puri and Jordan [8] have studied the propagation of plane waves under the 2TT....
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...Puri and Jordan [8] have studied the propagation of plane waves under the 2TT....
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