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-Şhulman (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.