State Space Approach to Electro-Magneto-Thermoelasticity with Energy Dissipation

In this article a two-dimensional problem of generalized thermoelasticity has been formulated with state space approach. In this formulation, the governing equations are transformed into a matrix differential equation whose solution enables us to write the solution of any two-dimensional problem in terms of the boundary conditions. The resulting formulation is applied to an isotropic half space problem under Green-Naghdi type-III model i.e., with energy dissipation theory of thermoelasticity in the presence of a magnetic field.  The bounding surface is traction free and subjected to a time dependent thermal shock. The solution for temperature distribution, displacements and stress components are obtained and presented graphically. The effect of magnetic field, electric field and phase velocity on the considered parameters is observed in the figures.