Kh. Lotfy

Two temperature generalized magneto-thermoelastic interactions in an elastic medium under three theories

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 (LS) and Green-Lindsay (GL) theories, as well as the classical dynamical coupled theory (CD). The medium is considered to be permeated by a uniform magnetic field. The general solution obtained is applied to a specific problem of a half-space and the interaction with each other under the influence of magnetic field subjected to one types of heating the thermal shock type. The normal mode analysis is used to obtain the exact expressions for the displacement components, force stresses, temperature and couple stresses distribution. The variations of the considered variables through the horizontal distance are illustrated graphically. Comparisons are made with the results between the three theories. Numerical work is also performed for a suitable material with the aim of illustrating the results.

Two-Dimensional Problem of Generalized Magneto-Thermoelasticity with Temperature Dependent Elastic Moduli for Different Theories

under the effect of temperature dependent properties is established. The modulus of elasticity is taken as a linear function on reference temperature. The formulation is applied under three theories of the generalized thermoelasticity: Lord‐Shulman and Green‐Naghdi (of type II) without energy dissipation, as well as the coupled theory. The normal mode analysis is used to obtain the expressions for the temperature, displacement components and the thermal stresses distributions. Numerical results are illustrated graphically for each problem considered. A Comparison is made with the results predicted by the three theories in the presence and absence of magnetic field and with the case where the modulus of elasticity is independent of temperature.

Mode-I crack in a two-dimensional fibre-reinforced generalized thermoelastic problem

A general model of the equations of the Lord—Şulman theory including one relaxation time and the Green—Lindsay theory with two relaxation times, as well as the classical dynamical coupled theory, are applied to the study of the influence of reinforcement on the total deformation for an infinite space weakened by a finite linear opening mode-I crack. We study the influence of reinforcement on the total deformation of rotating thermoelastic half-space and their interaction with each other. The material is homogeneous isotropic elastic half space. The crack is subjected to prescribed temperature and stress distributions. The normal mode analysis is used to obtain the exact expressions for displacement components, force stresses, and temperature. The variations of the considered variables with the horizontal distance are illustrated graphically. Comparisons are made with the results obtained in the three theories with and without rotation. A comparison is also made between the two theories for different depths.

Transient disturbance in a half‐space under generalized magneto‐thermoelasticity with a stable internal heat source under three theories

Purpose – The purpose of this paper is to study the transient waves caused by a line heat source with a stable internal heat source inside isotropic homogenous thermoelastic perfectly conducting half‐space permeate into a uniform magnetic field. The formulation is applied under three theories of generalized thermoelasticity Lord‐Shulman (L‐S) theory with one relaxation time, Green‐Lindsay (G‐L) theory with two relaxation times, as well as the classical dynamical coupled theory. The problem is reduced to the solution of three differential equations by introducing the elastic and thermoelastic potentials.Design/methodology/approach – The normal mode analysis is used to obtain the expressions. Numerical results are given and illustrated graphically. Comparisons are made with the results predicted by the three theories in the presence and absence of magnetic field and the internal heat source.Findings – The results are graphically described for the medium of copper. We can conclude that the magnetic field has...

Effect of rotation on plane waves in generalized thermo-microstretch elastic solid with a relaxation time

The present paper is aimed at studying the effect of rotation on the general model of the equations of generalized thermo-microstretch for a homogeneous isotropic elastic half-space solid whose surface is subjected to a Mode-I Crack problem considered. The problem is in the context of the generalized thermoelasticity Lord-Şhulman’s (L-S) theory with one relaxation time, as well as the classical dynamical coupled theory (CD) The normal mode analysis is used to obtain the exact expressions for the displacement components, force stresses, temperature, couple stresses and microstress distribution. The variations of the considered variables through the horizontal distance are illustrated graphically. Comparisons are made with the results in the presence and absence of rotation and in the presence and absence of microstretch constants between the two theories.

Gravitational effect and initial stress on generalized magneto-thermo-microstretch elastic solid for different theories

Abstract The present paper is aimed at studying the effect of gravity and initial stress on the general model of the equations of generalized magneto-thermo-microstretch for a homogeneous isotropic elastic half-space solid. The problem is in the context of the Lord–Şhulman and Green–Lindsay theories, as well as the coupled theory. The normal mode analysis is used to obtain the exact expressions for the displacement components, force stresses, temperature, couple stresses and microstress distribution. The variations of the considered variables perpendicular to the axis of rotation are illustrated graphically. Comparisons are made with the results in the presence and absence of gravity and magnetic field of a particular case for the generalized micropolar thermoelastic medium (without microstretch constants) between the three theories.

Two-temperature plane strain problem in a semiconducting medium under photothermal theory

Abstract In this investigation, we study the two-temperature problem with two-dimensional (2-D) deformations for a semi-infinite semiconducting medium at the free surface with the influence of mechanical force through a photothermal process. The harmonic wave method (Normal Mode analysis) has been used to get the exact expression of normal displacement, normal force stress, carrier density, and temperature distribution, and also the two-temperature coefficients ratios has been obtained analytically. The effects of several parameters as thermoelastic and thermoelectric coupling parameters and two-temperature parameter of this force on the displacement component, force stress, carrier density, and temperature distribution have been depicted graphically.

The effect of thermal relaxation times on wave propagation of micropolar thermoelastic medium with voids due to various sources

Purpose – The purpose of this paper is to formulate a model of the equations of a two‐dimensional problem with the deformation of micropolar generalized thermoelastic medium with voids under the influence of various sources in the context of the Lord‐Shulman, Green‐Lindsay theories, as well as the classical dynamical coupled theory.Design/methodology/approach – The normal mode analysis was used to obtain the exact expressions of the displacement components, force stress, coupled stress, change in volume fraction field and temperature distribution. Numerical results were given and illustrated graphically when the volume source was applied.Findings – The presence of voids plays a significant role on all the physical quantities. The value of normal displacement and normal force stress increases while the temperature, tangential force stress and the couple stress increase and then decrease due to the presence of voids. The value of all the physical quantities converges to zero with increase in distance z.Orig...

The effect of rotation on plane waves in generalized thermo-microstretch elastic solid with one relaxation time for a mode-I crack problem

The present paper is aimed at studying the effect of rotation on the general model of the equations of the generalized thermo-microstretch for a homogeneous isotropic elastic half-space solid, whose surface is subjected to a Mode-I crack problem. The problem is studied in the context of the generalized thermoelasticity Lord—Şhulmans (L—S) theory with one relaxation time, as well as with the classical dynamical coupled theory (CD). The normal mode analysis is used to obtain the exact expressions for the displacement components, the force stresses, the temperature, the couple stresses and the microstress distribution. The variations of the considered variables through the horizontal distance are illustrated graphically. Comparisons of the results are made between the two theories with and without the rotation and the microstretch constants.

Transient thermo‐elastic disturbances in a visco‐elastic semi‐space due to moving internal heat source

Purpose – This paper aims to investigate the transient disturbances created by an internal line heat source that suddenly starts moving uniformly inside a visco‐elastic half‐space.Design/methodology/approach – Generalised theory of thermo‐elasticity with relaxation time proposed by Lord‐Shulman is applied. The material of the semi‐infinite medium is an isotropic visco‐elastic solid of Kelvin‐Voight type. Fourier and Laplace transform techniques are used.Findings – Applying the Fourier and Laplace transform techniques, expressions for displacement components in the transformed domain are found. These expressions prove the existence of three waves – a modified thermal wave, a visco‐elastic wave of defused nature and a transverse visco‐elastic wave.Research limitations/implications – Surface displacement components were evaluated on the boundary for only a short time.Originality/value – The paper provides numerical results that are illustrated graphically to highlight the variations of surface displacement c...