载流导线在磁场中混沌运动区域分析

ANALYSIS OF CHAOTIC MOTION REGION OF WIRE CARRYING ELECTRIC CURRENT IN MAGNETIC FIELD

在考虑电磁场对结构变形影响基础上,假设导线变形为小变形,采用弦的模型建立了载流导线在磁场中的周期激励作用下的横向振动控制方程.利用伽辽金原理及Melnikov方法推导出了载流导线发生混沌运动的临界条件,并讨论了导线张力、导线距离、电流等因素对载流导线混沌运动区域的影响.得到了如下的结论:载流导线的混沌运动区域随导线张力、导线距离的增大而变大;电流小于某一值时,载流导线混沌运动区域随电流增大而减小.

Considering the influence of electromagnetic field on the structural deformation, and supposing that the wire＇s deformation was small, a natural lateral vibrant control equation of wire carrying electric current under the periodical excitation in the magnetic field was established by chord modeling. The critical condition to chaotic motion of the wire carrying electric current in the magnetic field was researched with Melnikov Method and Galer- kin Principle. And factors such as string tension, string distance and current that affected the chaotic motion re- gion were discussed. The results showed that the chaotic motion region of wire carrying electric current increased with the increasing of string tension and string distance respectively, and decreased with the increasing of electric current when the electric current was below a certain value.