Abo-el-nour N. Abd-alla

A PROBLEM OF GENERALIZED MAGNETOTHERMOELASTICITY FOR AN INFINITELY LONG, PERFECTLY CONDUCTING CYLINDER

This article concerns the investigation of the stress, temperature, and magnetic field in a transversely isotropic, elastic cylinder of infinite length and perfectly conducting material placed in a primary constant magnetic field when the curved surface of the cylinder is subjected to periodic loading. The analysis encompasses Lord and Shulman and Green and Lindsay theories of generalized thermoelasticity to account for the finite velocity of heat equation. The analysis of the numerical results for stress, temperature, and numerical values of the perturbed magnetic field in the free space is carried out at various points of the cylindrical medium. It is found that the effect of the applied magnetic field is an increase in the elastic wave velocity or, in other words, the increase of the solidity of the body. Furthermore, it has been shown graphically that the stress and perturbed magnetic field are modified due to the thermal relaxation time effect. In the absence of the magnetic field or relaxation times, our results reduce to those of generalized thermoelasticity and classical dynamical thermoelasticity, respectively.

THERMAL RELAXATION TIMES EFFECT ON RAYLEIGH WAVES IN GENERALIZED THERMOELASTIC MEDIA

Rayleigh waves in a half-space exhibiting generalized thermoelastic properties based on Green-Lindsay (G-L), Lord-Shulman (L-S), and classical dynamical coupled (C-D) theories are discussed. The phase velocity of Rayleigh waves in the previous three different theories has been obtained. A comparison is carried out between the phase velocities of Rayleigh waves, displacements, stresses, and temperature as calculated from the different theories of generalized thermoelasticity. The C-D theory is recovered as a special case. It appears, in particular, that the results obtained from G-L theory tend to those of L-S theory as the values of the two relaxation times become closer to each other. The second relaxation time is well pronounced when it becomes larger than the first one. Furthermore, it is found that the thermal relaxation times decrease the speed of the elastic waves and modify the phase velocities of the Rayleigh waves. The results obtained and the conclusions drawn are discussed numerically and illus...Rayleigh waves in a half-space exhibiting generalized thermoelastic properties based on Green-Lindsay (G-L), Lord-Shulman (L-S), and classical dynamical coupled (C-D) theories are discussed. The phase velocity of Rayleigh waves in the previous three different theories has been obtained. A comparison is carried out between the phase velocities of Rayleigh waves, displacements, stresses, and temperature as calculated from the different theories of generalized thermoelasticity. The C-D theory is recovered as a special case. It appears, in particular, that the results obtained from G-L theory tend to those of L-S theory as the values of the two relaxation times become closer to each other. The second relaxation time is well pronounced when it becomes larger than the first one. Furthermore, it is found that the thermal relaxation times decrease the speed of the elastic waves and modify the phase velocities of the Rayleigh waves. The results obtained and the conclusions drawn are discussed numerically and illustrated graphically. Relevant results of previous investigations are deduced as special cases.

Numerical simulations for the phase velocities and the electromechanical coupling factor of the Bleustein–Gulyaev waves in some piezoelectric smart materials:

In this paper, the propagation behavior of the surface Bleustein–Gulyaev (B-G) waves in a piezoelectric layered half-space is investigated. The governing equations of the coupled waves are obtained. The boundary conditions are assumed in such a way that the displacements, shear stress, electric potential, and electric displacements are continuous across the interface between the layer and the substrate together with the traction-free boundary at the surface of the layer. The electrically open and short conditions at the surface are adopted to solve the problem. The phase velocity is numerically calculated for the electric open and short cases for different thicknesses of the layer and wave number. The phase velocity equation of the B-G wave is obtained by an analytical technique when a layered half-space with an identical piezoelectric layer and substrate but with opposite polarization is utilized. The electromechanical coupling factor in the layered piezoelectric structures is discussed. The results obtained in this paper will be very useful for the engineering application of B-G waves.

A mathematical model for longitudinal wave propagation in a magnetoelastic hollow circular cylinder of anisotropic material under the influence of initial hydrostatic stress

In this paper, we built a mathematical model to study the influence of the initial stress on propagation of longitudinal waves in a hollow infinite circular cylinder in the presence of an axial initial magnetic field. The elastic cylinder is assumed to be made of a tetragonal system material. The problem is described by the equations of elasticity, taking into account the effect of the initial stress and the electro-magnetic equations of Maxwell. This requires the solution of the equations of motion in cylindrical coordinates with the z-axis directed along the axis of the cylinder. The displacement components will be obtained by founding the analytical solutions of the motion’s equations. The frequency equations have been obtained in the form of a determinant involving Bessel functions. The roots of the frequency equation give the values of the characteristic circular frequency parameters of the first three modes for various geometries when the initial hydrostatic stress is compression or tension. These roots, which correspond to various modes, are numerically calculated and presented graphically. This study shows that waves in a solid body propagating under the influence of an initial stress can differ significantly from those propagating in the absence of the initial stress. The results of this research are used in analyzing the relationship between magnetic field, the initial stress and the frequency equation and could lead to discussions for using the magnetic field and the initial stress in ultrasound imaging.

DEFORMATION OF AN INFINITELY LONG, DC CABLE WITH TEMPERATURE-DEPENDENT ELECTRIC CONDUCTIVITY OF THE INSULATION

We investigate the deformation of an infinitely long, circular cylindrical electric conductor carrying a uniform axial current, for the case when the electric conductivity of the coating is temperature dependent. This model conforms with the real situation for many of the existing modern dc cables with polyethylene coating. The distributions of temperature, magnetic field, stresses, and displacements in the cable are obtained and discussed under a thermal radiation condition at the boundary of the cable. In particular, it appears that there is a critical temperature for the ambient medium to the cable, above which no solution for the steady heat problem can exist and the thermal equilibrium of the cable is no longer fulfilled. A formula for the calculation of this critical value is given, which may turn out to be of practical importance for a reliable design of the cable. The obtained results also show that the electric conductivity of the coating strictly decreases as one moves from the core to the bound...We investigate the deformation of an infinitely long, circular cylindrical electric conductor carrying a uniform axial current, for the case when the electric conductivity of the coating is temperature dependent. This model conforms with the real situation for many of the existing modern dc cables with polyethylene coating. The distributions of temperature, magnetic field, stresses, and displacements in the cable are obtained and discussed under a thermal radiation condition at the boundary of the cable. In particular, it appears that there is a critical temperature for the ambient medium to the cable, above which no solution for the steady heat problem can exist and the thermal equilibrium of the cable is no longer fulfilled. A formula for the calculation of this critical value is given, which may turn out to be of practical importance for a reliable design of the cable. The obtained results also show that the electric conductivity of the coating strictly decreases as one moves from the core to the boundary of the cable in conformity with the behavior of temperature. Some numerical results are presented.

Shear horizontal waves in composite materials: Behavior under rotation and initial stress

The main scope of this paper is to present in a simple and concise way a mathematical model of composite materials able to describe the propagation of shear horizontal waves in the case where composite is rotating and subjected to an initial stress. This work is aimed at the relevant possibility to apply the obtained results for the establishment of high-achievement applications of piezoelectric and semiconductor composites and surface acoustic waves devices. We conclude by analyzing numerical computations in which the influence of the rotation, initial stress and electromagnetic boundary conditions are graphically observed.

Plane waves and eigenfrequency study in a transversely isotropic magneto-thermoelastic medium under the effect of a constant angular velocity

ABSTRACT In this article, we investigate the influence of (i) relaxation times according to the theory of Green–Lindsay, (ii) rotation, and (iii) magnetic field on incident and reflected plane waves in a transversely isotropic magneto-thermoelastic medium. We moreover make a numerical study to analyze the amplitude ratios for incident plane waves and a numerical eigenfrequency study presenting some shape modes for the displacement and temperature fields of a physical suitable cylindrical system. The medium rotates with a constant angular velocity, in the presence of a magnetic field orthogonal to the stress-free and thermally insulated plane. We solve the equations of this system and show the arising of three quasi-plane waves in the medium. The theoretical aspects of this article are focused on the reflection of these qp-waves from one of the surfaces of the medium, which we impose to be stress-free and thermally insulated: We obtain the reflection coefficients by numerical simulations considering a cylinder of cobalt.

Wave propagation in a generalized thermoelastic plate using eigenvalue approach

ABSTRACT In the present work, we obtain a dispersion relation for Rayleigh–Lamb wave propagation in a plate of thermoelastic material. For this aim, we consider the theory of generalized thermoelasticity with one relaxation time. The thickness of the plate is taken to be finite and the faces of the plate are assumed to be isothermal and free from stresses. We obtain the analytical solution for the temperature, displacement components, and stresses using an eigenvalue approach. Finally, we derive a dispersion relation for the plate in closed form taking into account isothermal boundary conditions for wave mode propagation. To obtain the phase velocity and attenuation coefficients of propagating wave mode, we use the function iteration numerical scheme to solve the complex dispersion relation. The phase velocity and attenuation coefficients for the first five modes of waves are represented graphically for Lord–Shulman and classical coupled dynamical theories.