State Space Approach for Conducting Magneto-Thermoelastic Medium with Variable Electrical and Thermal Conductivity Subjected to Ramp-Type Heating

Abstract

The equations of magneto-thermoelasticity with one relaxation time with variable electrical and thermal conductivity for one-dimensional problems are cast into matrix form using the state-space and Laplace transform techniques. The resulting formulation is applied to a half-space subjected to ramp-type heating and traction free. 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.

Keywords:

• Magneto-thermoelasticity
• Ramp-type heating
• Thermoelasticity