The Thermal Shock Response Of Electricmagneto-thermoelastic Coupled Problem

The governing equation of temperature field for the classical thermoelasticity theory is of the diffusion type predicting infinite speed of propagation for heat wave contrary to physical observations. The Fourier law that describes the relation between heat flux and temperature gradient is no longer suitable in transient heat propagation. To eliminate the paradox inherent in the classical theories, the generalized thermoelastic theories were developed in attempt to amend the classical thermoelasticity. Lord and Shulman (L-S) introduced one thermal relaxation time and Green and Lindsay (G-L) introduced two to establish generalized thermoelastic theory respectively. Both theories can characterize heat disturbance propagating with finite velocity in medium, which is so called second sound effect.Based on the generalized themoelcastic theories, the dynamic thermoelastic as well as magneto-thermoelastic problems of finite rods are analyzed and discussed in this paper. First, the generalized thermoelastic coupled problem for a isotropic rod fixed at both ends and subjected to a moving heat source is discussed; Second, the generalized magneto-thermoelastic coupled problem for a isotropic rod fixed at both ends and subjected to a moving heat source; Finally, the generalized magneto-thermoelastic coupled problem for a rod subjected to a moving heat source with temperature-dependent properties is analyzed. In the case of temperature-independent properties, dynamic response of a isotropic rod fixed at both ends located applied magnetic field or not is dealt with respectively; and in the study of temperature-dependent properties, dynamic response of a isotropic rod fixed at both ends located applied magnetic field or not is discussed respectively.During the study of one-dimensional boundary value of a isotropic rod fixed at both ends subjected a moving heat source at one end, the generalized thermoelastic coupled governing equations of L-S type is established. The problem is solved by means of Laplace transform and numerical inversion of the transforms technologies. Analytic solutions for stress, displacement and temperature are obtained. From the distributions of the considered variables, we can find the variations increase as the moving heat source velocity increases.During the analysis of a rod fixed at the ends subjected to a moving heat source located the applied magnetic field, the generalized magnetic-thermoelastic coupled governing equations of L-S type is formulated. The problem is solved by means of Laplace transform and numerical inversion of the transforms technologies, obtained the distributions of the stress, displacement and temperature. From the distributions of the considered variables, it is easy to find the wave type heat conduction and magnetic-thermoelastic coupled effects, and observe that the applied magnetic field has no effect on the temperature, however it significantly influences the variations of displacement and stress. This indicates that the magnetic field acts to damp the thermal expansion deformation of the rod.During the study of dynamic response of a finite rod subjected a moving heat source with temperature-dependent properties, the modulus of elasticity of the rod is taken as a linear function of initial reference temperature, the generalized thermoelastic coupled governing equations of L-S type is established. Similarly, The problem is solved by means of Laplace transform and numerical inversion of the transforms technologies, obtained the distributions of the stress, displacement and temperature. From the distributions of the considered variables, the displacement and stress are influenced by the dependence of the modulus of elasticity on reference temperature markedly, but the temperature is not nearly affected. It can be also found that the thermal relaxation time has certain effect on the variations, the peak value of variations increase as the thermal relaxation increases, but the change tendency is not influenced.During the discussion of a rod fixed at the ends subjected a moving heat source with temperature-dependent properties located the applied magnetic, the generalized magnetic-thermoelastic coupled governing equations of L-S type is formulated, obtained the distributions of the stress, displacement and temperature. From the distributions, it can be found the influence of magnetic and the dependence of the modulus of elasticity on reference temperature to variations, they act to damp the temperature, stress and displacement.