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

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.