横向磁场中载流薄板模态截断问题研究

Modal Truncation Problems of a Current Carrying Plate in a Transver Magnetic Field

根据板壳理论与磁弹性理论,在不考虑感应电场,仅考虑机械场与磁场的相互耦合作用情况下,在薄板非线性运动方程、物理方程、几何方程、洛仑兹力表达式及电动力学方程的基础上,建立在横向磁场和机械载荷共同作用下的大挠度载流矩形薄板的非线性运动方程。以三边简支一边自由矩形薄板为例,给出板的单模态运动方程和双模态运动方程。利用数学计算软件,采用四阶Ronger-Kuta数值方法,模拟非线性系统在单、双模态位移模式下的时程图、庞加莱截面图、相轨迹图。讨论电磁参数和外载荷参数对板在单、双模态位移模式下的非线性行为的影响及差异。结果表明,这些参数对薄板的运动有较大的影响,通过调整电磁参数可控制系统的混沌运动,以实现对系统运动特性的控制。

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.