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.