Propagation of waves in magneto-thermo-viscoelastic solids subjected to a uniform magnetic field

Abstract The propagation of magneto-thermo-mechanical ( MTM ) plane waves in electrically and thermally conductive magneto-thermo-viscoelastic ( MTVE ) unbounded solids is investigated with account for the mutual effects of the magnetic, thermal and strain fields. Concerning the mutual and thermo-electric effects in isotropic solids the governing equations are first linearized. In the linearization, the material is assumed to be subjected to a uniform and primary magnetic field in any direction while the material undergoes infinitesimal deformations. It is shown that the governing equations at the intermediate state are fulfilled by the presumed MTM -fields. Furthermore, the dispersion relation which allows us to consider the entire frequency range, the effect of the magnetic field and some nondimensional material parameters is obtained. Therefore, several modes of MTM -waves arise depending upon the direction of the magnetic field such as the uncoupled magnetic and mechanical S -mwaves, the coupled S -wave, the modified mechanical P -and thermal waves, and the modified and coupled MTM -waves. It is seen that all modes of the wave are dispersive and dissipative due to the conductivity and the viscosity of the material. Then the phase velocities and the attenuation constants for the coupling modes are obtained, and some limiting values are discussed. From the expressions follow, in particular, the results for the elastic case, the propagation of mechanical waves in nonconductive materials.