中文摘要：

利用Karman关于板的大挠度理论,考虑涡电流在板中引起的Lorentz力,导出了在横向磁场和横向载荷共同作用下薄板的非线性运动方程.借助Bubnov-Galerkin法将非线性偏微分方程转化为含三次非线性项的常微分方程.在定性分析的基础上,利用次谐轨道的Melnikov函数给出了发生Smale马蹄型混沌运动的阈值条件,进而数值计算了系统的分岔图、相应的相图、Poincaré映射和时程曲线,给出了混沌运动的数字特征.分析结果表明：磁感应强度和外载荷都会影响系统的振动特性.

英文摘要：

By using Karman’s plate theory of large deflection,the nonlinear equation of motion of a thin metal plate with the coaction of a transverse uniform magnetic field and a transverse load is established. These equations consider the magnetic Lorentz force induced by the eddy current. Based on the Bubnov-Galerkin method,the nonlinear partial differential equation is transformed into a third-order nonlinear ordinary differential equation. By using the sub-harmonic orbit Melnikov function method,the criterion of the Smale-horseshoe chaos is also acquired. Furthermore,the chaotic motion is numerically simulated with Matlab. The bifurcation diagram,the phase curve,the Poincaré map and the evolution curve are calculated. The digital characteristics of the chaotic motions are provided based on the analysis. The analysis results show that the magnetic induction intensity and the external load may affect the vibration of the system.