The Generalized Magneto-thermoviscoelastic Dynamic Response Of Rod

The classical thermoelastic theory based on the Fourier law of heat conduction is accurate enough in general conditions, but this theory suggests that thermal equilibrium is established in an instant, which implies that the speed of propagation for heat wave is infinite. It is not applicable to characterize the heat conduction phenomena in ultra-high or ultra-low heat environment any more, where heat is believed to propagate with finite speed. To eliminate this contradiction with the actual situation, the generalized thermoelasticity theories were developed in 1960's. At present, there are two typical generalized thermoelastic theories known as Lord and Shulman theory and Green and Lindsay theory. Lord and Shulman (L-S) introduced one thermal relaxation time and Green and Lindsay (G-L) introduced two to establish generalized thermoelastic theory respectively.Based on the generalized thermoelasticity theories, the dynamic magneto-thermoelastic responses of a semi-infinite rod and a finite rod are analyzed and discussed in this paper. First the dynamic thermalviscoelastic responses of a semi-infinite isotropic rod placed in a magnetic field and subjected to a moving heat source is investigated. Second, the generalized magneto-thermoelastic coupled problem for an isotropic rod fixed at both ends and subjected to a moving heat source is investigated; Finally, the generalized magneto-thermo(visco)elastic coupled problems for a rod subjected to a moving heat source with temperature-dependent properties are analyzed.During the study of the generalized magneto-thermoviscoelastic coupled problem for a semi-infinite rod and a finite rod, both Lord and Shulman(L-S) theory and Green and Lindsay(G-L) theory were applied to investigating the dynamic thermalviscoelastic responses of a semi-infinite isotropic rod placed in a magnetic field and subjected to a moving heat source. Comparisons were made between the results obtained from the above theories and the classical coupled thermoelastic theory. The generalized thermoviscoelastic coupled governing equations for the rod were formulated. By means of Laplace transformation and numerical Laplace inversion the governing equations were solved. Numerical calculation for stress, displacement and temperature within the rod was carried out and displayed graphically. The effects of time, moving heat source speed and the size of the magnetic field on temperature, stress and temperature was discussed .During the study of dynamic response of a finite rod subject to 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 dynamic thermalelastic responses of the rod is analyzed by Lord and Shulman(L-S) theory and both Lord and Shulman(L-S) theory and Green and Lindsay(G-L) theory are applied to investigating the dynamic thermalviscoelastic responses of the rod. Similarly, the problem is solved by means of Laplace transform and numerical inversion of the transform technology, and the distributions of the stress, displacement and temperature are obtained. From the distributions of the considered variables, the displacement and stress are influenced by the dependence of the magnetic field and the modulus of elasticity on reference temperature markedly, but the temperature is nearly not 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.