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•

Discontinuities in generalized thermoelastic wave propagation in a semi-infinite piezoelectric rod

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M. C. Majhi

01 Jan 1995-Technical Physics

TL;DR: In this paper, generalized thermoelastic wave propagation in a semi-infinite piezoelectric rod, which is heated by some time-dependent sources of heat distributed over a certain region, has been investigated.

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Abstract: The theory of thermoelasticity taking into account the time needed for the acceleration of heat flow has produced tremendous interest in recent times. Several models of this generalized theory have been proposed by various authors. In the prresent papers generalized thermoelastic wave propagation in a semi-infinite piezoelectric rod, which is heated by some time-dependent sources of heat distributed over a certain region, has been investigated. The points of discontinuity in the temperature field and the corresponding jumps have been determined and illustrated graphically.

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28 citations

Additional excerpts

...Majhi [43] studied the transient thermal response of a semi-infinite piezoelectric rod subjected to a local heat source along the length direction by introducing a potential function and applying the LS theory....
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Journal Article•DOI•

Variational and Reciprocal Principles in Two-Temperature Generalized Thermoelasticity

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Roushan Kumar¹, Rajesh Prasad¹, Santwana Mukhopadhyay¹•Institutions (1)

Banaras Hindu University¹

09 Feb 2010-Journal of Thermal Stresses

TL;DR: In this paper, the authors established a variational principle of convolutional type and a reciprocal principle in the context of linear theory of generalized thermoelasticity for a homogeneous and isotropic body.

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Abstract: The aim of the present work is to establish a variational principle of convolutional type and a reciprocal principle in the context of linear theory of two-temperature generalized thermoelasticity, for a homogeneous and isotropic body.

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28 citations

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

...[56, 57] established variational and reciprocal principles and some theorems in two-temperature generalized thermoelasticity....
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On mittag-lettler-type function in fractional evolution processes

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F Mainardi, R Gorenflo

01 Jan 2000

TL;DR: In this article, a variety of fractional evolution processes are reviewed, whose solutions turn out to be related to Mittag-Leffler type functions, and the chosen equations are the simplest of the fractional calculus and include the Abel integral equations of the second kind.

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Abstract: Abstract We review a variety of fractional evolution processes (so defined being governed by equations of fractional order), whose solutions turn out to be related to Mittag-Leffler-type functions. The chosen equations are the simplest of the fractional calculus and include the Abel integral equations of the second kind, which are relevant in typical inverse problems, and the fractional differential equations, which govern generalized relaxation and oscillation phenomena.

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26 citations

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

...The notation Iξ is the Riemann–Liouville fractional integral, introduced as a natural generalization of the well-known n-fold repeated integral Inf (t) written in a convolution-type form as in Mainardi and Gorenflo [66], which is written as follows Inf (t) = 1 (n) ∫ t 0 (t − τ )n−1f (τ )dτ , 0 n ≤ 2 = f (t), n = 0 (2) where (n) is the Gamma function....
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...The notation I is the Riemann–Liouville fractional integral, introduced as a natural generalization of the well-known n-fold repeated integral Inf (t) written in a convolution-type form as in Mainardi and Gorenflo [66], which is written as follows...
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Journal Article•DOI•

Two-Temperature Generalized Thermoelastic Interactions in an Infinite Body with a Spherical Cavity

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Sukla Banik¹, Mridula Kanoria¹•Institutions (1)

University of Calcutta¹

31 May 2011-International Journal of Thermophysics

TL;DR: In this article, the authors derived the displacement, stress, conductive temperature, and temperature in an infinite isotropic elastic body with a spherical cavity in the context of the two-temperature generalized thermoelasticity theory (2TT).

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Abstract: This paper is concerned with the determination of the thermoelastic displacement, stress, conductive temperature, and thermodynamic temperature in an infinite isotropic elastic body with a spherical cavity in the context of the two-temperature generalized thermoelasticity theory (2TT). The two-temperature Lord-Shulman (2TLS) model and two-temperature Green–Naghdi (2TGN) models of thermoelasticity are combined into a unified formulation introducing the unified parameters. The medium is assumed initially quiescent. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain which is then solved by (a) the state-space approach and (b) the eigenvalue approach for any set of boundary conditions. The general solution obtained is applied to a specific problem when the boundary of the cavity is subjected to thermomechanical loading. The numerical inversion of the transform is carried out using Fourier-series expansion techniques. The computed results for thermoelastic stresses, conductive temperature, and thermodynamic temperature are shown graphically for the Lord Shulman model and for two models of Green–Naghdi and the effects of two temperatures are discussed. A comparative study of the two methods has also been carried out.

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24 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•

Two-Temperature Generalized Thermopiezoelasticity for One Dimensional Problems – State Space Approach

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Hamdy M. Youssef, E. Bassiouny

01 Jan 2008-computational methods in science and technology

TL;DR: In this paper, the theory of two-temperature generalized thermoelasticity is used to solve boundary value problems of one dimensional piezoelectric half-space with heating its boundary with different types of heating.

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Abstract: The theory of two-temperature generalized thermoelasticity, based on the theory of Youssef is used to solve boundary value problems of one dimensional piezoelectric half-space with heating its boundary with different types of heating. The governing equations are solved in the Laplace transform domain by using state-space approach of the modern control theory. The general solution obtained is applied to a specific problems of a half-space subjected to three types of heating; the thermal shock type, the ramp type and the harmonic type. The inverse Laplace transforms are computed numerically using a method based on Fourier expansion techniques. The conductive temperature, the dynamical temperature, the stress and the strain distributions are shown graphically with some comparisons.

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22 citations

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

...For computational purposes, the values of the material constants have been taken as follows [52] F0 = 1, = 0....
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...Youssef and Bassiouny [52] solved a boundary value problem of a one-dimensional piezoelectric half-space by heating its boundary using different types of heating by using two-temperature generalized theory in the context of the LS model....
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