The Magnetic Elastic Buckling Bifurcation Of The Thin Rectangular Plate With Current Carrying

Because the magnetic elasticity theory research by the very significant problem with the coupling effect, it is bound to energy, transportation, national defense, and so have a wide range of applications. Therefore, the theory of its related research has very important significance. At present, domestic and foreign scholars on the role of mechanical load plates, shells chaotic motion made a lot of research. However, the research of mechanical load on the electromagnetic field coupled with the bifurcation are also unusual. In the view of this, the paper studies the buckling bifurcation issues of the thin current carrying rectangular plate coupled with the mechanical load on the electromagnetic field. The main work aspects on the following:Firstly, the paper introduces briefly the background and significance of the research, the description of bifurcation and its basic theory, the basic knowledge of mathematics related to the bifurcation.Secondly, for two thin current carrying rectangular plates ,one simply supported at three edges and another simply supported on the edge and fixed on the edge, the dynamic buckling equation was derived by using Galerkin method on the basis of the nonlinear magneto-elastic equations of motion, physical equations, expression of Lorentz forces and the electrodynamics equations. For the thin current carrying rectangular plates under the two boundary conditions, the bifurcation points, bifurcation conditions and the type of bifurcation have been gotten through discussing the existence and stability of equilibrium state when considering the thin plate applied static load. And when considering the thin plate applied dynamic load, the dynamic bifurcation equation and the bifurcation diagram have been gotten under the two boundary conditions using LS method. And the paper gets the bifurcation points, bifurcation conditions of the thin current carrying rectangular plates coupled with the mechanical load on the electromagnetic field under the two boundary conditions.Finally, For the aluminum sheet under the two boundary conditions, given the relevant parameters, using the computer program of Matlab language, it calculates the value of critical load when the bifurcation occurred, as well as the curve of relationion and the change patterns between the critical load and current density, the magnetic intensity and geometry of the plate.