横向磁场激励下铁磁梁式板的混沌运动分析  

ANALYSIS OF CHAOTIC MOTIONS OF GEOMETRICALLY NONLINEAR FERROMAGNETIC BEAM-PLATES EXICITED BY TRANSVERSE MAGNETIC FIELDS

作　　者：高原文[1] 周又和[1] 郑晓静[1] 

机构地区：[1]兰州大学力学系,兰州730000

出　　处：《力学学报》2002年第1期101-108,共8页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家杰出青年科学基金(10025205);教育部高校骨干教师基金; 清华大学教育部破坏力学重点实验室开放课题资助项目~~

摘　　要：在磁体力分布的磁弹性理论模型和磁场准静态假定模式基础上，对于处在周期时变磁场 中的不可移简支铁磁梁式板非线性磁弹性动力特性进行定性与定量分析．首先利用磁场的摄 动技术和结构变形的模态法，导出了关于模态坐标的非线性动力方程；然后利用Ｍｅｌｎｉｋｏｖ方 法，从理论上给出这一磁弹性动力系统可能出现混沌运动的必要条件及参数范围；最后采用变 步长Ｒｕｎｇｅ－Ｋｕｔｔａ数值积分方法对其磁弹性相互作用的混沌现象进行了定量搜索与模拟，并 利用其轨迹的Ｐｏｉｎｃａｒｅ截面图与Ｌｉａｐｕｎｏｖ指数加以判断．结果表明磁弹性简支梁式板在横 向周期时变磁场中存在混沌吸引子，且在机械阻尼很小时其混沌吸引子表现出稠的特性．Based on the theoretical model of Magnetic Body Force for magnetoelastic interaction of ferromagnetic plates in magnetic fields, and the assumption of quasi-static state to magnetic fields, a theoretical analysis is presented in this paper to the nonlinear dynamic system of a geometrically nonlinear ferromagnetic beam-plate with simply supported and unmovable ends in an exciting transverse magnetic field with periodic variation. First of all, the perturbation technique is employed for analyzing distribution of magnetic fields varying with deflection of the plate. Secondly, a necessary condition of existence of chaotic motions in the magnetoelastic dynamic system is obtained by means of the Melnikov Method. Finally, the chaotic motions of the magnetoelastic system are simulated or searched by the Runge-Kutta method with variable steps, and the Poincaré map and the Liapunov exponents to the trace of motions are employed to evaluate if a chaotic motion appears. The numerical results indicate that there exist some chaotic motions in the magnetoelastic system of the ferromagnetic beam-plates in transverse magnetic fields of periodic varying, and that the chaotic motion is dense when the mechanical damping in the system is small enough in the chaotic range of parameters.

关 键 词：几何非线性 横向磁场激励 混沌运动 数值模拟 铁磁梁式板 磁弹性理论模型 摄动技术 非线性科学 周期时变磁场 LIAPUNOV指数 

分 类 号：TM27[一般工业技术—材料科学与工程] O327[电气工程—电工理论与新技术]