Rotation and Hall Current on Rayleigh Waves in Transversely Isotropic Visco-Thermoelastic Half-Space with and without Energy Dissipation

In the current work, Rayleigh waves in a homogeneous transversely isotropic viscoelastic rotating medium with two temperatures are investigated in the presence of the combined effects of magnetic field and Hall currents. The Green-Naghdi Theories of thermoelastic type-II and type-III are the theories of thermoelasticity to which the formulation is applied [1]. Mathematically, secular equations are obtained at the insulated and stress-free limits. Determinant of Rayleigh wave secular equation, Rayleigh wave velocity and attenuation coefficient are computed numerically and depicted graphically for a specific model. Some special cases are also deduced from the present investigation. The results obtained indicate to the strong effect for the rotation and viscosity on the Rayleigh waves propagation phenomenon that agree with the results obtained if the new parameters neglected. A comparison has been made between the current estimation and the previous works obtained by others that indicate to the strong impact for the external parameters on the phenomenon of Rayleigh waves in transversely isotropic visco-thermoelastic either with or without energy dissipation considering rotation and hall current.