Magneto-Elasticity Bifurcation Of A Thin Current Carrying Rectangular Plate And The Modal Analysis Of The Chaotic Motion

Bifurcation and Chaos are the most important and basic features in nonlinear systems. Almost all involved the fields of nonlinear science, there are bifurcation phenomena and chaotic motions. Based on the analysis and summary of nonlinear differential bifurcation and chaotic dynamical systems, for the electromagnetic field in the transverse magnetic field and mechanical load coupled large deflection under current-carrying non-linear behavior of rectangular plates has been 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 and expression of electromagnetic force are introduced, lamella non-linear equations of motion are derived and the nonlinear magnetic thin flexible bifurcation related to chaos theory and research methods are described.Secondly, based on mechanical and magnetic shell theory of elasticity in the transverse magnetic field and mechanical load together downloads flow rectangular plates of non-linear equations of motion, one edge free and others simply supported was taken as computational example, boards are discussed in a single, dual-mode displacement mode state of motion. And plate in a single and dual-mode displacement mode state of motion was given using the Matlab. From the simulation results can be obtained, in some regions, you can use single-mode displacement of the structure of non-linear movement pattern analysis and in some regions must be dual-mode displacement mode or higher order displacement model analysis, otherwise may lead to wrong conclusions.Finally, the nonlinear equations of motion of a rectangular thin current plate simply supported at each edge was established when the plate applied mechanical load in a transverse magnetic field,using mechanics of plates and shells and theory of the magnetic-elasticity,the bifurcation of rectangular plates, chaotic motion and single-, dual-mode displacement mode comparison was studied. In nonlinear systems, single and dual-mode time-shift mode, map, Poincare sections, phase locus was given using the Matlab. Further from the theory and numerical simulation, using of single and dual-mode displacement model to study the nonlinear behavior differences was discussed.