Generalized magneto-thermoelastic medium with variable material properties subjected to ramp-type heating

摘要

The equations of magneto-generalized thermoelasticity with one relaxation time with variable electrical and thermal conductivity for one-dimensional problems are cast into a matrix form using the state-space approach and Laplace transform techniques. The resulting formulation is applied to a problem of a half space where the bounded plane is subjected to a ramp-type heating and a traction free. This takes place when a constant magnetic field permeates the medium in the absence of an external electric field. The inversion of the Laplace transform is carried out using a numerical approach. Numerical results for the temperature, the displacement, and the stress distributions are given and illustrated graphically.