Abstract
In this paper, having or lacking a rotating, magnetic field, and a time-dependent source of heat on a two-dimensional homogeneous, isotropic, and thermoelastic half-space was illustrated. The governing equations were formulated in the considering Maxwell's stresses. The surface boundary settings were explored considering the thermoelasticity model of Green and Naghdi (type II). The techniques of the eigenvalue method and the normal mode analysis were utilized to resolve the non-dimensional coupled equations. We analyzed theoretically and computed numerically the rotation, time, wave number, frequency, and magnetic field. A comparison between having or lacking of the rotation was made with the results obtained. The displacement components, temperature, dilatation, and average of the normal stress were displayed in graphs to illustrate the physical meaning of the wavenumber, frequency, rotation, magnetic field, and time-dependent heat source. Normal stresses have been displayed graphically to show the physical meaning of the magnetic field, rotation, frequency, wave number, and time-dependent heat source. The results obtained show that having rotation, magnetic field, and time affects significantly eigenvalue issue, especially in astrophysics, aircraft, engineering, astronomy, petroleum extracting, and structures.