Mohamed I. A. Othman

Electromagneto-thermoelastic plane waves with two relaxation times in a medium of perfect conductivity

The model of the two-dimensional equations of generalized magneto-thermoelasticity with two relaxation times in a perfectly conducting medium is established. The normal mode analysis is used to obtain the exact expressions for the temperature distribution, thermal stresses and the displacement components. The resulting formulation is applied to two different concrete problems. The first deals with a thick plate of perfect conductivity subjected to time-dependent heat source on each face, while the second concerns the case of a heated punch moving across the surface of a semi-infinite thermoelastic half-space of perfect conductivity subject to appropriate boundary conditions. Numerical computations for the horizontal component of the displacement are carried out and represented graphically for each problem. A comparison was made with the results obtained in the absence of a magnetic field.

Lord-Shulman theory under the dependence of the modulus of elasticity on the reference temperature in two-dimensional generalized thermoelasticity

The model of the equations of generalized thermoelasticity based on Lord-Shulman theory in an isotropic elastic medium under the dependence of the modulus of elasticity on the reference temperature is established. The normal mode analysis is used to obtain the expressions for the temperature, the horizontal component of displacement, and thermal stress. The resulting formulation is applied to two different concrete problems. The first concerns the case of a heated punch moving across the surface of a semi-infinite thermoelastic half-space subject to appropriate boundary conditions. The second deals with a thick plate subject to a time-dependent heat source on each face. Numerical results are illustrated graphically for each problem considered. Comparisons are made with the results obtained in the case of temperature independence of the modulus of elasticity.

ELECTROMAGNETO-THERMOELASTIC PLANE WAVES WITH THERMAL RELAXATION IN A MEDIUM OF PERFECT CONDUCTIVITY

The model of the two-dimensional equations of generalized magneto-thermoelasticity with one relaxation time in a perfectly conducting medium is established. The normal mode analysis is used to obtain the exact expressions for the temperature distribution, thermal stresses, and the displacement components. The resulting formulation is applied to three different concrete problems. The first deals with a thick plate of perfect conductivity subjected to a time-dependent heat source on each face; the second concerns the case of a heated punch moving across the surface of a semi-infinite thermoelastic half-space of perfect conductivity subject to appropriate boundary conditions; and the third problem deals with a plate with thermo-isolated surfaces subjected to time-dependent compression. Numerical results are given and illustrated graphically for each problem. Comparisons are made with the results predicted by the coupled theory and with the theory of generalized thermoelasticity with one relaxation time.The model of the two-dimensional equations of generalized magneto-thermoelasticity with one relaxation time in a perfectly conducting medium is established. The normal mode analysis is used to obtain the exact expressions for the temperature distribution, thermal stresses, and the displacement components. The resulting formulation is applied to three different concrete problems. The first deals with a thick plate of perfect conductivity subjected to a time-dependent heat source on each face; the second concerns the case of a heated punch moving across the surface of a semi-infinite thermoelastic half-space of perfect conductivity subject to appropriate boundary conditions; and the third problem deals with a plate with thermo-isolated surfaces subjected to time-dependent compression. Numerical results are given and illustrated graphically for each problem. Comparisons are made with the results predicted by the coupled theory and with the theory of generalized thermoelasticity with one relaxation time.

State space approach to two-dimensional generalized thermo-viscoelasticity with two relaxation times

The model of the two-dimensional equations of generalized thermo-viscoelasticity with two relaxation times is established. The state space formulation for two-dimensional problems is introduced. Laplace and Fourier integral transforms are used. The resulting formulation is applied to a problem of a thick plate subject to heating on parts of the upper and lower surfaces of the plate that varies exponentially with time. The Fourier transforms are inverted analytically. A numerical method is employed for the inversion of the Laplace transforms. Numerical results are given and illustrated graphically for the problem considered. Comparisons are made with the results predicted by the coupled theory.

State space approach to two-dimensional electromagneto-thermoelastic problem with two relaxation times

Abstract The model of the two-dimensional equations of generalized magneto–thermoelasticity with two relaxation times in a perfectly conducting medium are established. The method of the matrix exponential, which constitutes the basis of the state space approach of modern theory, is applied to the non-dimensional equations. Laplace and Fourier integral transforms are used. The resulting formulation is applied to a problem of a thick plate subject to heating on parts of the upper and lower surfaces of the plate that varies exponentially with time. Numerical results are given and illustrated graphically for the problem considered. A comparison was made with the results obtained in the absence of a magnetic field.

State space approach to generalized thermo-viscoelasticity with two relaxation times

The model of the equation of generalized thermo-viscoelasticity with two relaxation times is established. The state space formulation for thermo-viscoelasticity with two relaxation times is introduced. The formulation is valid for problems with or without heat sources. The resulting formulations together with the Laplace transform technique are applied to a variety of problems. The solutions to a thermal shock problem and to a problem of a layer media both without heat sources are obtained. Also a problem with a distribution of heat sources is considered. A numerical method is employed for the inversion of the Laplace-transforms. Numerical results are given and illustrated graphically for the problems considered. Comparisons are made with the results predicted by the coupled theory.

Generalized thermo-viscoelastic plane waves with two relaxation times

The model of the two-dimensional generalized thermo-viscoelasticity with two relaxation times (Green and Lindsay theory) is established. The normal mode analysis is used to obtain the exact expressions for the temperature distribution, thermal stresses and the displacement components. The resulting formulation is applied to three different concrete problems. The first deals with a thick plate subjected to a time-dependent heat source on each face. The second concerns to the case of a heated punch moving across the surface of a semi-infinite thermo-viscoelastic half-space subjected to appropriate boundary conditions and the third problem deals with a plate with thermo-isolated surfaces subjected to a time-dependent compression. Numerical results are given and illustrated for each problem. Comparisons are made with the results predicted by the coupled theory.

Generalized thermoelasticity of the thermal shock problem in an isotropic hollow cylinder and temperature dependent elastic moduli

In this paper, we construct the equations of generalized thermoelasticity for a non-homogeneous isotropic hollow cylider with a variable modulus of elasticity and thermal conductivity based on the Lord and Shulman theory. The problem has been solved numerically using the finite element method. Numerical results for the displacement, the temperature, the radial stress, and the hoop stress distributions are illustrated graphically. Comparisons are made between the results predicted by the coupled theory and by the theory of generalized thermoelasticity with one relaxation time in the cases of temperature dependent and independent modulus of elasticity.

THE DEPENDENCE OF THE MODULUS OF ELASTICITY ON THE REFERENCE TEMPERATURE IN GENERALIZED THERMOELASTICITY

The model of the equations of generalized thermoelasticity with two relaxation times in an isotropic elastic medium with temperature-dependent mechanical properties is established. The modulus of elasticity is taken as a linear function of reference temperature. The state-space approach developed in [Bahar and Hetnarski, J. Thermal Stresses , vol. 1, pp. 135-146, 1978] is adopted for the solution of one-dimensional problems. The technique is applied to a thermal shock problem, a problem of a layer medium, and a problem for infinite space in the presence of heat sources. Numerical results are illustrated graphically for the problems considered. A comparison was made with the results obtained in the case of temperatureindependent mechanical properties.

Generalized Electromagneto‐Thermoelastic Plane Waves by Thermal Shock Problem in a Finite Conductivity Half‐Space with One Relaxation Time

A two‐dimensional coupled problem in electromagneto‐thermoelasticity for a thermally and electrically conducting half‐space solid whose surface is subjected to a thermal shock is considered. The problem is in the context of the Lord and Shulman’s generalized thermoelasticity with one relaxation time. There acts an initial magnetic field parallel to the plane boundary of the half‐space. The medium deformed because of thermal shock and due to the application of the magnetic field, there result an induced magnetic and an induced electric field in the medium. The Maxwell’s equations are formulated and the electromagneto‐thermoelastic coupled governing equations are established. The normal mode analysis is used to obtain the exact expressions for the considered variables. The distributions of the considered variables are represented graphically. From the distributions, it can be found the wave type heat propagation in the medium. This indicates that the generalized heat conduction mechanism is completely diffe...