Thermo-Mechanical and Electro-Magnetic Field

Since from the 19th century, the phenomenons of coupling between the thermo-mechanical and the electro-magnetic behavior of materials have been studied. By the middle of the 20th century, the first applications of piezoelectric materials were being found in hydrophones. The concept of electro-magnetic composite materials has been arisen by the last two centuries. Such composites can exhibit field coupling that is not present in any of the monolithic constituent materials. These so called 'Smart' materials and composites have applications in ultrasonic imaging devices, sensors, actuators, transducers, and many other emerging components.

Magneto-electro-elastic materials are used in various applications. Due to the ability of converting energy from one kind to another (among mechanical, electric, and magnetic energies), these materials have been used in high-tech areas such as lasers, supersonic devices, microwave, infrared applications, etc. Furthermore, magneto-electro-elastic materials possess coupling behavior among mechanical, electric, and magnetic fields and are inherently anisotropic. Problems related to the wave propagation in thermoelastic or magneto-thermo-elastic solids using these generalized theories have been studied by several authors.

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Among them, Paria has presented some ideas about magneto-thermo-elastic plane waves. Neyfeh and Nemat-Nasser have studied thermo-elastic waves and electro-magneto-elastic waves in solids with a thermal relaxation time. Ezzat have studied electromagneto-thermo-elastic plane waves, with thermal relaxation in a medium of perfect conductivity. Othman and Song  used the models of the generalized magneto-thermo-elasticity to study the reflection of magneto-thermo-elastic waves from a rotating elastic half space. The generalized magneto-thermoelasticity used in this paper is based on the Lord-Shulman theory with one relaxation time, Green-Lindsay theory with two relaxation time and the dynamical coupled (CD) theory  also acquired the reflection coefficients and the effect of applied magnetic field, rotation and frequency are studied and are shown graphically studied the propagation of a magneto-thermo elastic plane waves in an initially stressed, homogeneous orthotropic, conducting half-space under a magnetic field , rotation and gravity field.

The generalized theory of thermoelasticity is employed, by assuming the mechanical behavior as dynamic, to study the problem. The Lames potential is used to obtain the frequency equation that determines the velocity of Rayleigh waves that obtained as a real part and the attenuation coefficient as an imaginary part under the rotation, magnetic field, initial stress and gravity field. Numerical results have been given and illustrated graphically for each case considered. Dispersion curves of wave propagation are represented graphically in different theories of thermo elasticity. The results indicate that the effect of rotation, initial stress and gravity field are very pronounced. Comparison is made with the results predicted by the theory of thermo elasticity in the absence of rotation, initial stress and gravity field. [4] Studied the effect of magnetic field on the general model of equations of rotating generalized thermo-micro stretch for a homogeneous isotropic elastic half-space solid whose surface is subjected to a Mode-I Crack in the context of the Green and Naghdi theory. The normal mode analysis is used to obtain the exact expressions for the displacement components, force stresses, temperature, couple stresses, and micro stress distribution.

The variations of the considered variables through the horizontal distance are illustrated graphically. In the presence and absence of the rotation, the results are compared for the two cases: case (1) for the generalized micropolar thermoelasticity elastic medium (without micro stretch constants) between the two types (II, III); case (2) for the generalized microstretch thermo-elasticity elastic medium (without micropolar constants) between the two types (II, III). The model of the equations of generalized magneto-thermoelasticity for a perfect conducting isotropic thermoelastic media is studied by. This model is applied to solve a problem of an infinite body with a cylindrical cavity in the presence of an axial uniform magnetic field. The boundary of the cavity is subjected to a combination of thermal and mechanical shock acting for a finite period of time.

The solution is obtained by a direct approach by using the thermo elastic potential function. Laplace transform techniques are used to derive the solution in the Laplace transform domain. The inversion process is carried out using a numerical method based on Fourier series expansions. Numerical computations for the temperature, the displacement and the stress distributions as well as for the induced magnetic and electric fields are carried out and represented graphically. The results predicted by the generalizations, Lord-Shulman theory, and Green-Lindsay theory as well as to the coupled theory are also compared. Parvez and Shekhar  used the Biots incremental deformation theory for finding the algebraic expressions of the reflection coefficients and energy ratios when plane waves of and type are incident on the initially stressed dissipative half-space with stress free boundaries. The dispersion equations for reflection coefficients and energy ratios of incident and waves on the free surface of the initially stressed dissipative medium have been derived and observed that in presence of initial stresses, magnetic field and rotation of the medium must affect the reflection coefficients and energy shares of reflected plane waves.