Dynamics Response And Analysis To Generalized Electromagneto-thermoelastic Medium

The governing equation of temperature field for the classical thermoelasticity theory is the diffusion type predicting infinite speed of propagation for heat wave, which is contrary to experimental 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 thermoelastic theories, by means of Laplace transform and numerical Laplace inversion, the dynamic thermoelastic as well as magneto-thermoelastic problems of a semi-infinite rotating rod and an infinite rotating cylinder are analyzed and discussed in this work. And by means of direct finite element method, the generalized magneto-thermoelastic coupled dynamic problems for a thin slim strip, a half-space and a rotating half-space are investigated in the context of L-S theory. In this work, the generalized magneto-thermoelastic coupled problem for a semi-infinitely long rotating rod subjected to a thermal shock is considered first; Second, the generalized magneto-thermoelastic coupled problem for an infinite long rotating cylinder whose surface subjected to a thermal shock is analyzed; Last, the direct finite element method is applied to solving generalized magneto-thermoelastic coupled dynamic problems. In the case of considering rotation effect, dynamic responses of a semi-infinite long rotating rod and an infinite long rotating cylinder are analyzed respectively; and in the part of applying direct finite element method to solving generalized coupled problems, dynamic responses of a thin slim strip, a half-space and a rotating half-space are discussed respectively.In the process of analyzing the dynamic response of a semi-infinite long rotating rod subjected to a thermal shock and an 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 its numerical inversion. The distributions of the dimensionless temperature, dimensionless displacement, dimensionless stress , dimensionless induced magnetic field and dimensionless induced electric field are obtained and presented graphically. From the distributions of the considered variables, it is easy to find the wave type heat conduction and magnetic-thermoelastic coupled effects, and rotation acting to significantly increase the magnitude of the real part of displacement, stress, induced magnetic field and induced electric field and insignificantly affect the magnitude of temperature. During the analysis of an infinite long rotating cylinder subjected to a thermal shock and an applied magnetic field, the formulation is proceeded by combining L-S theory and G-L theory in the same set of governing equations in terms of suitable parameters. The problem is solved by means of Laplace transform and its numerical inversion, and the distributions of the dimensionless temperature, dimensionless displacement and dimensionless stress are obtained. From the distributions of the considered variables, it can be found the wave type heat conduction and magneto-thermoelastic coupled effects, and rotation acting to significantly increase the magnitude of the real part of displacement, stress, and induced electric field and induced magnitude field and no affect the magnitude of temperature.In order to avoid the accuracy loss encountered in the process of numerical inversion of integral transformation method adopted to solve generalized thermoelastic coupled problems in the context of Lord-Shulman (L-S) theory, the direct finite element method is used to solve L-S type generalized magneto-thermoelastic coupled dynamic problems for a thin slim strip, a half space and a rotating half space subjected to a thermal shockand an applied magnetic field respectively. The L-S type generalized thermoelastic coupled governing equations, the general form of virtual displacement principle as well as the corresponding finite element equations are formulated. The distributions of dimensionless temperature, dimensionless displacement, dimensionless stress and dimensionless induced magnitude field are displayed graphically. From the distribution of temperate, the unique characteristic of heat wave can be observed clearly in the location of heat wave front where a sharp change of temperature occurs. From the distributions of the considered variables, it is easy to find the wave type heat conduction and magnetic-thermoelastic coupled effects, and rotation acting to decrease the magnitude of the real part of displacement, stress, and induced magnitude field, and not to affect the magnitude of temperature.