Bifurcation And Chaos Of Current-Carrying Thinplate In Electromagnetic Field

Bifurcation and Chaos is the most important and basic features in nonlinear systems. Almost all inveleved the fields of nonlinear science, there are bifurcation phenomena and chaotic motions. It is very common that the rods, plates and shells work in an electromagnetic environment as structural components with the development of modern advanced technology. One of the basic characters when an electromagnetic field and a mechanical field coupled teghter is to be a new nonlinear system.Based on the analysis and summary of nonlinear differential bifurcation and chaotic dynamical systems,the nonlinear behavior of a thincurrent-carrying plate applied mechanical load in a transvers magnetic field were studied. The main work of our research is summarized in the following parts.Firstly, the chaotic motion domestic, the foreign research situation and primary content of our research are introduced. And Menikov method which determined the chaotic motion is introduced. At same time, several kinds of Menikov functions used widely are shown here.Secondly, for the thin plate with these boundaryies: (1)one edge free and others simply supported,(2)one oppoisite edges fixed and the other two simply supported, chaotic motion under its single modal displacement pattern was analysised using Melnikov function method. The balance points of the nonlinear dynamic system were gotten in the case of non-disturbance. The critical condition of chaos in the sense of Smale horseshoes of the system was also obtained using Melnikov function method when a disturbance happened. And chaos charts satisfied this condition are given using the Matlab.Finally, for the thin current-carrying plate with the same boundaries mentioned before, chaotic motion under its double modal displacement pattern was analysised using the average method. The bifurcation point of the strip plate under the dual-mode displacement was obtained and the stability of bifurcation point was also discussed using the averaging method. The differences of the simulation to the nonlinear behavior of a system using single-, dual-mode displacement mode were analyzed theoretically.