In this study, we proposed an analytical solution for eddy currents as well as electromagnetic forces of a conductive circular plate in a time varying magnetic field. Specifically, an analytical series solution for eddy currents in a circular plate subjected to an axisymmetrie time varying magnetic field has been proposed based on the T-method that has been widely used in the eddy current analysis of conductive and superconductive structures. Accordingly, the dynamic response, the dynamic instability and the magnetic damping of a circular plate in a transverse transient magnetic field as well as a stationary in-plane magnetic field have also been obtained. The analytical series solution proposed in this work as well as the subsequent numerical analysis not only confirmed the emergence of dynamic instability of a circular plate in a strong transverse magnetic field, but also demonstrated the existence of magneto-damping of a circular conductive plate in an in-plane magnetic field. The method developed in this paper provides a potential new possible way by which the analysis of the electromagnetic coupling problems of conductive structures can be simplified.
Yuanwen Gao1 Bang Xu(Key Laboratory of Mechanics on Western Disaster and Environment,College of Civil Engineering and Mechanics,Lanzhou University,Lanzhou 730000,China)
Based on the Boltzmann transport equation of electrons and taking the scattering effect of electrons in the grain boundary as the boundary conditions of electrons transport in the grain, we presented a theoretical model for the Seebeck coefficient of bulk poly- crystalline thermoelectric materials, and applied it to studying the grain size effect on the Seebeck coefficient. Then we discussed the effects of transmissivity, temperature and the mean free path of electrons on the size effect. The results show that the proposed theoretical model is reasonable and effective and the predicted results for the Seebeck coefficient are in good agreement with the experimental data reported in literature. The bulk polycrystalline materials have notable (big) grain size effects on the Seebeck coefficient, and the influences of transmissivity, temperature and the mean free path of electrons on the Seebeck coefficient are also significant.
