The Dynamic Responses Of Generalized Electromagneto-thermoelastic Problems With Diffusion For Half Spaces

With the rapid developments of the ultrashort pulse laser technology and wide application of the microelectronic devices, thermo-mechanical coupling problem under ultrashort time has attracted more and more attention. To eliminate the existing intrinsic paradox in the conventional thermoelastic theory and accurately describe the thermo-mechanical coupling phenomenon involving very short time situation, researchers have established different generalized thermoelastic theories to describe the wave effect of heat propagation(i.e., the speed of heat propagation is finite). At present, the main generalized thermoelasticity theories widely used in scientific research were developed by Lord and Shulman (L-S), Green and Lindsay (G-L) and Green and Naghdi (G-N) respectively. The above mentioned theories can characterize the finite speed of heat propagation in the medium to show the second sound effect in solid. Simultaneously, the multi-fields coupling effect is considered in these theories.Diffusion phenomenon widely exists in nature and in industrial process and it is an extremely important physical and mechanical process in the migration and transportation of material particles. Generally speaking, diffusion can be defined as the random walk of an ensemble of material particles (eg., atoms, molecules) from regions of high concentration to regions of lower concentration. In1855, Fick established Fick’s law to describe the diffusion process, which is similar to the Fourier’s heat conduction law in nature. Nevertheless, Fick’s law doesn’t take the mutual interplays between the introduced substance and the substrate into consideration. In2004, Sherief et al. proposed the generalized thermoelastic diffusion theory by combining L-S theory and Fick’s law. This theory can describe the multi-fields (i.e., deformation field, temperature field and diffusion field) coupling effects and the nature of these three fields propagating as waves with finite speeds in solid medium.In present thesis, the dynamic responses of generalized thermoelastic problems with diffusion for half-spaces are investigated by means of the normal mode analysis as well as the hybrid Laplace-finite element method respectively in the context of the generalized thermoelastic diffusion theory. The concrete contents include the following two problems:(1) the dynamic response of a two-dimensional generalized electromagneto-thermoelastic problem for a half-space with diffusion is investigated. The half-space is initially placed in an external magnetic field with constant intensity and its bounding surface in contact with a permeating substance is taken to be traction free and subjected to a time-dependent thermal load and a time-dependent chemical shock. Normal mode analysis is applied to solving the problem and a corresponding eighth-order characteristic equation is established to obtain the exact solutions of the considered variables. The results show the nature that thermoelastic wave as well as diffusive wave propagates with finite speed respectively. It can also be observed that the magnitudes of all the considered variables increase with time;(2) the dynamic response of a two-dimensional generalized thermoelastic problem with diffusion for a half-space is considered. The half-space is subjected to a thermal shock and a chemical potential shock on its bounding surface. The hybrid Laplace transform-finite element method is used to solve the problem and the numerical solutions are obtained in Laplace domain. The results show that the non-zero values of all the considered variables are only in a bounded region and vanish identically beyond this region, and the propagating speed of diffusive wave is larger than that of thermoelastic wave. The results obtained from the above problems show that taking the multi-fields coupling effect into account in the investigation of generalized thermoelastic diffusive problems has much significant theoretical and practical values, especially, in the functional and safety design of structures serving in complex environments.