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Journal ArticleDOI

A three-dimensional thermoelastic problem for a half-space without energy dissipation

01 Feb 2012-International Journal of Engineering Science (Pergamon)-Vol. 51, pp 310-325
TL;DR: In this paper, a three-dimensional problem for a homogeneous, isotropic and thermoelastic half-space subjected to a time-dependent heat source on the boundary of the space, which is traction free, is considered in the context of the Green and Naghdi model II (thermasticity without energy dissipation).
About: This article is published in International Journal of Engineering Science.The article was published on 2012-02-01. It has received 71 citations till now. The article focuses on the topics: Thermoelastic damping & Dissipation.
Citations
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Journal ArticleDOI
TL;DR: A three-dimensional model of the generalized thermoelasticity without energy dissipation under temperature-dependent mechanical properties is established and the modulus of elasticity is taken as a linear function of the reference temperature.
Abstract: A three-dimensional model of the generalized thermoelasticity without energy dissipation under temperature-dependent mechanical properties is established. The modulus of elasticity is taken as a linear function of the reference temperature. The resulting formulation in the context of Green and Naghdi model II is applied to a half-space subjected to a time-dependent heat source and traction free surface. The normal mode analysis and eigenvalue approach techniques are used to solve the resulting non-dimensional coupled equations. Numerical results for the field quantities are given in the physical domain and illustrated graphically. The results are also compared to results obtained in the case of temperature-independent modulus of elasticity.

93 citations

Journal ArticleDOI
TL;DR: In this article, the fractional order Green-Lindsay model of generalized thermoelasticity with voids (FGLV) subjected to instantaneous heat sources in a plane area has been established using the Riemann-Liouville fractional integral operator and applied to solve a problem of determining the distribution of temperature, the volume fraction field, the deformation and the stress field in an infinite elastic medium.

57 citations

Journal ArticleDOI
TL;DR: The present paper is concerned with the investigation of disturbances in a homogeneous, isotropic reference temperature-dependent elastic medium with fractional order generalized thermoelastic diffusion and analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained.
Abstract: The present paper is concerned with the investigation of disturbances in a homogeneous, isotropic reference temperature-dependent elastic medium with fractional order generalized thermoelastic diffusion. The formulation is applied to the generalized thermoelasticity based on the fractional time derivatives under the effect of diffusion. The analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained in the physical domain by using the normal mode analysis technique. These expressions are calculated numerically for a copper-like material and depicted graphically. Effect of fractional parameter and presence of diffusion is analyzed theoretically and numerically. Comparisons are made with the results predicted by the fractional and without fractional order in the presence and absence of diffusion.

41 citations

Journal ArticleDOI
TL;DR: In this paper, a fractional order Lord & Shulman model of generalized thermoelasticity with voids subjected to a continuous heat sources in a plane area has been established using the Caputo fractional derivative and applied to solve a problem of determining the distributions of the temperature field, the change in volume fraction field, and the deformation and the stress field in an infinite elastic medium.
Abstract: In the present work, a fractional order Lord & Shulman model of generalized thermoelasticity with voids subjected to a continuous heat sources in a plane area has been established using the Caputo fractional derivative and applied to solve a problem of determining the distributions of the temperature field, the change in volume fraction field, the deformation and the stress field in an infinite elastic medium. The Laplace transform together with an eigenvalue approach technique is applied to find a closed form solution in the Laplace transform domain. The numerical inversions of the physical variables in the space-time domain are carried out by using the Zakian algorithm for the inversion of Laplace transform. Numerical results are shown graphically and the results obtained are analyzed .

40 citations

Journal ArticleDOI
Kh. Lotfy1
TL;DR: Magneto-thermoelastic interactions in an isotropic homogeneous elastic half-space with two temperatures are studied using mathematical methods under the purview of the Lord-Shulman and Green-Lindsay theories, as well as the classical dynamical coupled theory.

39 citations


Cites methods from "A three-dimensional thermoelastic p..."

  • ...One can find several two-dimensional works based on the generalized thermoelasticity by using the normal mode analysis in the literatures Ezzat and Abd Elall [30], Othman and Lotfy [31–32], Lofty and Othman [33], Lofty [34] and Sarkar and Lahiri [35]....

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References
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Journal ArticleDOI
TL;DR: In this article, a generalized dynamical theory of thermoelasticity is formulated using a form of the heat transport equation which includes the time needed for acceleration of heat flow.
Abstract: In this work a generalized dynamical theory of thermoelasticity is formulated using a form of the heat transport equation which includes the time needed for acceleration of the heat flow. The theory takes into account the coupling effect between temperature and strain rate, but the resulting coupled equations are both hyperbolic. Thus, the paradox of an infinite velocity of propagation, inherent in the existing coupled theory of thermoelasticity, is eliminated. A solution is obtained using the generalized theory which compares favourably with a known solution obtained using the conventional coupled theory.

3,266 citations

Journal ArticleDOI
TL;DR: In this article, a unified treatment of thermoelasticity by application and further developments of the methods of irreversible thermodynamics is presented, along with a new definition of the dissipation function in terms of the time derivative of an entropy displacement.
Abstract: A unified treatment is presented of thermoelasticity by application and further developments of the methods of irreversible thermodynamics. The concept of generalized free energy introduced in a previous publication plays the role of a ``thermoelastic potential'' and is used along with a new definition of the dissipation function in terms of the time derivative of an entropy displacement. The general laws of thermoelasticity are formulated in a variational form along with a minimum entropy production principle. This leads to equations of the Lagrangian type, and the concept of thermal force is introduced by means of a virtual work definition. Heat conduction problems can then be formulated by the methods of matrix algebra and mechanics. This also leads to the very general property that the entropy density obeys a diffusion‐type law. General solutions of the equations of thermoelasticity are also given using the Papkovitch‐Boussinesq potentials. Examples are presented and it is shown how the generalized coordinate method may be used to calculate the thermoelastic internal damping of elastic bodies.

2,287 citations

Journal ArticleDOI
TL;DR: In this article, a general uniqueness theorem for linear thermoelasticity without energy dissipation is proved and a constitutive equation for an entropy flux vector is determined by the same potential function which also determines the stress.
Abstract: This paper deals with thermoelastic material behavior without energy dissipation; it deals with both nonlinear and linear theories, although emphasis is placed on the latter. In particular, the linearized theory of thermoelasticity discussed possesses the following properties: (a) the heat flow, in contrast to that in classical thermoelasticity characterized by the Fourier law, does not involve energy dissipation; (b) a constitutive equation for an entropy flux vector is determined by the same potential function which also determines the stress; and (c) it permits the transmission of heat as thermal waves at finite speed. Also, a general uniqueness theorem is proved which is appropriate for linear thermoelasticity without energy dissipation.

1,649 citations

Journal ArticleDOI
TL;DR: In this article, the authors focused on the thermal properties of the constitutive response functions in the context of both nonlinear and linear theories, and provided an easy comparison of the one-dimensional version of the equation for the determination of temperature in the linearized theory.
Abstract: This paper is concerned with thermoelastic material behavior whose constitutive response functions possess thermal features that are more general than in the usual classical thermoelasticity. After a general development of the constitutive equations in the context of both nonlinear and linear theories, attention is focused on the latter. In particular, the one-dimensional version of the equation for the determination of temperature in the linearized theory provides an easy comparative basis of its predictive capability: In one special case where the Fourier conductivity is dominant, the temperature equation reduces to the classical Fourier law of heat conduction, which does not permit the possibility of undamped thermal waves; however,'in another special case in which the effect of conductivity is negligible, the equation has undamped thermal wave solutions without energy dissipation.

1,143 citations

Journal ArticleDOI
TL;DR: In this paper, the basic postulates of the purely mechanical theory for a continuum (including its specialization for a rigid body) are re-examined in the context of flow of heat in a rigid solid with particular reference to the propagation of thermal waves at finite speed.
Abstract: This paper is mainly concerned with a re-examination of the basic postulates and the consequent procedure for the construction of the constitutive equations of material behaviour in thermomechanics. However, the implication of the basic postulates and the significance of the related procedure for the development of the constitutive equations is also illustrated in some detail in the context of flow of heat in a rigid solid with particular reference to the propagation of thermal waves at finite speed. More specifically, after briefly examining the nature of the basic equations of motion for a system of particles within the scope of the classical newtonian mechanics, the basic postulates of the purely mechanical theory for a continuum (including its specialization for a rigid body) is re-examined. This includes some differences from the usual procedure on the subject. Next, thermal variables are introduced and after observing a useful analogy between the thermal and mechanical variables, a discussion of a theory of heat (or a purely thermal theory) is provided which differs from the usual development in the classical thermodynamics. A detailed application of the latter development is then made to the problem of heat flow in a stationary rigid solid using several different and well-motivated constitutive equations. Special cases of these include linearized theories of the classical heat flow by conduction and of heat flow transmitted as thermal waves. The remainder of the paper is concerned with thermal mechanical theory of deformable media along with discussions of a number of related issues on the subject.

1,065 citations