磁场中轴向运动条形板强非线性超谐共振及混沌运动

针对磁场环境中周期外载作用下轴向运动导电条形板的非线性振动及混沌运动问题进行研究。应用改进多尺度法对横向磁场中条形板的强非线性振动问题进行求解，得到超谐波共振下系统的分岔响应方程。根据奇异性理论对非线性动力学系统的普适开折进行分析，求得含两个开折参数的转迁集及对应区域的拓扑结构分岔图。通过数值算例，分别得到以磁感应强度、轴向拉力、激励力幅值和激励频率为分岔控制参数的分岔图和最大李雅普诺夫指数图，以及反映不同运动行为区域的动力学响应图形，讨论分岔参数对系统呈现的倍周期和混沌运动的影响。结果表明，可通过相应参数的改变实现对系统复杂动力学行为的控制。

STRONGLY NONLINEAR SUPERHARMONIC RESONANCE AND CHAOTIC MOTION OF AXIALLY MOVING STRIP THIN PLATE IN MAGNETIC FIELD

In this paper, the nonlinear vibration and chaotic motion of the axially moving current-conducting strip thin plate with an external harmonic force in magnetic field is studied. Improved multiple-scale method is employed to derive the strongly nonlinear superharmonic resonance bifurcation-response equation of the strip thin plate in transverse magnetic field. By using the singularity theory, the corresponding transition variety and bifurcation which contain two parameters of the universal unfolding for this nonlinear system are obtained. Numerical simulations are carried out to plot the bifurcation diagrams, corresponding maximum Lyapunov exponent diagrams and dynamical response diagrams with respect to the bifurcation parameters such as magnetic induction intensity, axial tension, external force amplitude and external excited frequency. The influences of different bifurcation parameters on period doubling motion and chaotic motion behaviors of superharmonic resonance system are analyzed. The results show that the complex dynamic behaviors of resonance system can be controlled by changing the corresponding parameters.