The theory of thermomechanical-electromagnetic coupling was constructed. The finite element analysis of thermo-visco-elastic-plastic-electromagnetic continuum was formulated. Then the problem of wave propagation in this continuum was solved in two stages. In Stage I, a nearly static thermomechanical solution of a hollow cylinder, subject to twist and temperature gradient, was obtained. Then, in Stage II, the problem of wave propagation of scalar and vector potentials, due to deformation and temperature gradient, was solved. In the second approach, in Stage I, the static electric field and static magnetic field are obtained through static scalar and vector potentials, then in Stage II, the dynamic solutions of temperature, plastic strains, von Mises stress, and current were solved.
Song et al. (Thu,) studied this question.