输电线路导线舞动中的混沌运动研究  

Study on chaos in galloping of the transmission line

作　　者：侯磊[1] 陈予恕[1] 

机构地区：[1]哈尔滨工业大学航天学院,黑龙江哈尔滨150001

出　　处：《振动工程学报》2014年第1期75-83,共9页Journal of Vibration Engineering

基　　金：国家自然科学基金重点资助项目(10632040)

摘　　要：导线舞动是导致输电线路发生灾难性事故的一个重要原因。探讨了导线舞动中可能存在的运动模式,特别是混沌运动的存在性。首先采用Lagrange方程建立了包含横向和扭转两个自由度的导线运动微分方程,然后采用多尺度法分别对方程在1∶1,2∶1及3∶1内共振情况下进行了求解,得到了各自的平均方程,并根据振幅的可解条件在Ω-U平面内构造出Arnold舌头曲线。根据Arnold舌头法,由不同内共振情况下Arnold舌头的叠加情况,将Ω-U参数平面划分为6个区域。最后,通过数值计算分别研究了6个参数区域中存在的运动模式,风速取U=30.5m/s时,得到了混沌运动。对于该混沌运动发生机理的一种解释为,在特定参数下,导线系统同时存在3种内共振形式,三者之间相互转化导致系统表现出复杂的运动模式。Galloping is one of the important causes to catastrophic accidents of transmission lines.This paper aims to investigate the motion patterns that may exist in the conductor galloping,especially the existence of chaotic motion.First,the two-degreeof-freedom differential equations of motion containing lateral and torsional are established by using Lagrange equation.Next,the equations are solved for 1 ∶ 1,2 ∶ 1 and 3 ∶ 1 resonance cases by using the multiple scales method and the corresponding averaged equations are obtained.Based on the amplitude solvable conditions,Arnold tongue curves are constructed in the Ω-U plane.According to Arnold tongue method,the Ω-U plane is divided into 6 regions on the basis of different overlapping cases among the three Arnold tongues.Finally,the motion patterns in the six parameter regions are studied by numerical experiments.Meanwhile,the chaotic motion is found when setting U=30.5 m/s and Ω=3.178 1.It is an explanation of the chaotic motion that the three resonance patterns may coexist when certain parameters are chosen,and the mutual transformation of them leads to the complex motion patterns of the system.

关 键 词：非线性振动 导线舞动 混沌 内共振 Arnold舌头法 

分 类 号：O322[理学—一般力学与力学基础] TM752.5[理学—力学]