关键词: 薄板, 磁弹性, 大挠度, 非线性, 混沌

Abstract: According to the theory of plates and shells and the magnetic-elasticity theory, without considering the induced electric field, and in the case of only considering the coupling of mechanical field and the magnetic field, the nonlinear kinetic equation of a current carrying plate applied mechanical load in a transverse magnetic field with large deflection is given out based on the nonlinear motion equations of a thin plate, physical equations, geometric equations, Lorentz force expression and power dynamic equation. Take a thin current carrying plate simply supported at three edges and the other’s free as an example, the single or double mode nonlinear kinetic equations of the plate are shown here. The time history diagram, Poincare section plot and the phase trajectory of the nonlinear system with single or double mode large deflection are drawn through applied 4 orders Ronger-Kuta method by using calculating program. The differences and influence of the electro-magnet parameter and mechanical load to the nonlinear characters of the system are also discussed. The results show that the variation of these parameters will lead to significant influence on the motion of the plate. Through adjusting electro-magnet parameter, the chaos motion of the system can be controlled. Furthermore, the aim of controlling the characters of the chaotic motion of the system can be reached.

Key words: Chaos, Large deflection, Magnet-elasticity, Nonlinear, Thin plate