Magneto–thermoelastic behavior of an orthotropic hollow cylinder based on Lord–Shulman and Green–Lindsay theories

In this research, an analytical solution based on the finite Hankel transformation was developed for the magneto–thermoelasticity problem in an orthotropic hollow cylinder. Two second sound theories of generalized thermoelasticity, the Lord–Shulman and Green–Lindsay theories, were considered in a unified form to study the response of the cylinder subjected to thermal and mechanical loads, as well as a magnetic field. The inner boundary of the cylinder was subjected to a thermal shock in the form of heat flux, while the temperature was kept constant on the outer boundary. The displacement and traction boundary conditions were considered for the inner and outer surfaces of the cylinder, respectively. Closed-from solutions were presented for the magneto–thermoelasticity equations, and effects of the magnetic field intensity on the response of the cylinder were investigated. It was shown that considering finite velocity for the temperature causes propagation and reflection of the thermal wave in the cylinder. The impact of considering orthotropic material properties for the structure was studied, and the results were compared with known data from the literature, revealing strong agreement.