Effect of the thermal relaxation and magnetic field on generalized micropolar thermoelasticity
12 May 2016-Journal of Applied Mechanics and Technical Physics (Pleiades Publishing)-Vol. 57, Iss: 1, pp 108-116
TL;DR: In this article, the generalized micropolar magneto-thermoelasticity for a thermally and perfectly conducting half-space is studied, where the initial magnetic field is parallel to the boundary of the half-spaces.
Abstract: The model of generalized micropolar magneto-thermoelasticity for a thermally and perfectly conducting half-space is studied. The initial magnetic field is parallel to the boundary of the half-space. The formulation is applied to the generalized thermo-elasticity theories of Lord and Shulman, Green and Lindsay, as well as to the coupled dynamic theory. The normal mode analysis is used to obtain expressions for the temperature increment, the displacement, and the stress components of the model at the interface. By using potential functions, the governing equations are reduced to two fourth-order differential equations. By numerical calculation, the variation of the considered variables is given and illustrated graphically for a magnesium crystal micropolar elastic material. Comparisons are performed with the results predicted by the three theories in the presence of a magnetic field.
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TL;DR: In this paper, the effect of memory-dependent derivative and the influence of thermal loading due to laser pulse on the wave propagation of generalized micropolar thermoelasticity was investigated.
Abstract: The purpose of this paper is to introduce the phase-lag models (Lord-Shulman, dual-phase-lag and three-phase-lag) to study the effect of memory-dependent derivative and the influence of thermal loading due to laser pulse on the wave propagation of generalized micropolar thermoelasticity. The bounding plane surface is heated by a non-Gaussian laser beam with a pulse duration of 10 nanoseconds.,The normal mode analysis technique is used to obtain the exact expressions for the displacement components, the force stresses, the temperature, the couple stresses and the micro-rotation. Comparisons are made with the results predicted by three theories of the authors’ interest. Excellent predictive capability is demonstrated at a different time also.,The effect of memory-dependent derivative and the heat laser pulse on the displacement, the temperature distribution, the components of stress, the couple stress and the microrotation vector have been depicted graphically.,Some particular cases are also deduced from the present investigation.,The numerical results are presented graphically and are compared with different three theories for both in the presence and absence of memory-dependent effect and with the results predicted under three theories for two different values of the time.
32 citations
TL;DR: In this paper, the effect of hall current and rotation on a magneto-thermoelastic solid with microtemperatures and voids was investigated, and the normal mode analysis was used to obtain the exact expressions for the considered variables.
Abstract: In this study, the effect of hall current and rotation on a magneto-thermoelastic solid with microtemperatures and voids are investigated. The medium is permeated by a strong transverse magnetic field imposed perpendicularly on the displacement plane, the induced electric field being neglected. The normal mode analysis is used to obtain the exact expressions for the considered variables. Numerical simulated results are depicted graphically to show the effect of hall current, voids parameter and rotation on resulting quantities. The results indicate that the effect of hall current, voids parameter and rotation are very pronounced. Some particular cases of special interest have been deduced from the present investigation.
21 citations
TL;DR: In this article, an analysis of wave propagation in a microstretch elastic medium in the context of the Green-Naghdi (GN) theory is presented, and the dissipation and influence of gravity on reflected waves have also been investigated.
Abstract: This paper presents an analysis of wave propagation in a microstretch elastic medium in the context of the Green–Naghdi (GN) theory. Moreover, the dissipation and the influence of gravity on reflected waves have also been investigated. In the present article, five reflected waves propagate into the medium for any incident wave. The problem is solved numerically, and the amplitude ratios are graphically represented allowing for a comparison between the simple GN theory and the case in which one considers the effect of gravity on waves.
10 citations
TL;DR: In this article, a generalized thermoelasticity model for an isotropic medium with mechanical properties that are dependent on temperature is established, and the results are analyzed in a deeper manner by comparing them with unique cases of absence of the magnetic field, temperature dependent properties of the body, and two types of mechanical loads.
Abstract: A new model of equations of generalized thermoelasticity for an isotropic medium with mechanical properties that are dependent on temperature is established. The present problem is a generalization of the three-phase-lag model, Lord and Shulman's coupled theory. The elasticity modulus is a reference temperature function which is linear. Analytical expressions of the considered variables are obtained by using the Laplace–Fourier transforms technique. The results are analysed in a deeper manner by comparing them with unique cases of absence of the magnetic field, temperature-dependent properties of the body, and two types of mechanical loads. The most significant points are highlighted.
7 citations
TL;DR: In this paper, the effects of the kernel function, time-delay parameter, magnetic field and thermoelastic coupling parameter on the variations of different field quantities inside the half-space are analyzed graphically.
5 citations
References
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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
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
01 Sep 1965
TL;DR: In this article, a special class of micro-elastic materials called Micropolar Solids are presented for couple stress and distributed body couples, and the couple stress theory is shown to emanate as a spacial case of the present theory.
Abstract: : Equations of motion, constitutive equations and boundary conditions are presented for a special class of micro-elastic materials called Micropolar Solids. These solids respond to micro-rotational motions and spin inertia and can support couple stress and distributed body couples. The couple stress theory is shown to emanate as a spacial case of the present theory when the motion is constrained so that micro- and macro-rotations coincide. Several energy and uniqueness theorems are given.
929 citations
350 citations
350 citations