覆冰输电导线舞动的Noether对称性和守恒量  

The Noether Symmetry and Conserved Quantity of Galloping Iced Power Transmission Lines

作　　者：郑明亮 刘洁 邓斌 ZHENG Mingliang;LIU Jie;DENG Bin(College of Mechanical&Electrical Engineering,Jinggangshan University,Ji’an,Jiangxi 343009,P.R.China;School of Electrical and Mechanical Engineering,Wuxi Taihu University,Wuxi,Jiangsu 214064,P.R.China)

机构地区：[1]井冈山大学机电工程学院,江西吉安343009 [2]无锡太湖学院机电工程学院,江苏无锡214064

出　　处：《应用数学和力学》2021年第3期275-281,共7页Applied Mathematics and Mechanics

基　　金：江苏省高等学校自然科学基金(18KJB460027,20KJD4600001)。

摘　　要：为克服传统输电导线非线性振动响应数值模拟的非保结构缺点,研究了输电导线在覆冰和大风激励条件下双向舞动中的Noether对称性和守恒量.首先,考虑空气动力和导线几何的非线性,依据分析力学方法建立了垂向与扭振两自由度舞动模型;其次,引进群分析理论,根据不变性原则给出了系统存在Noether对称性的条件以及相应守恒量的形式;最后,构造了一种保守恒量离散数值算法.研究表明,用Noether对称性理论研究机械结构非线性动力学系统力学特性,能保系统内在结构属性,方法新颖,适用范围广,结果可靠准确.To overcome the non-structure-preserving drawbacks in traditional numerical simulation of transmission-line nonlinear vibration responses,the Noether symmetry and conserved quantity of transmission lines’2-way galloping under ice and wind excitation were studied.Firstly,in view of the nonlinearity of the aerodynamic force and the line geometry,a 2-DOF galloping model of vertical and torsional vibrations was established based on the analytical mechanics method.Secondly,the group analysis theory was introduced,and the condition and the conserved quantity of the Noether symmetry were given according to the invariance principle.Finally,a conserved quantity-preserving discrete numerical algorithm was constructed.The dynamic characteristics of the nonlinear mechanical structure were studied with the Noether symmetry theory.The results show that,the proposed novel method is structure-preserving in a wide range of application,and is reliable and accurate.

关 键 词：导线舞动 非线性特性 NOETHER对称性 守恒量 

分 类 号：Th122[机械工程—机械设计及理论] O316[理学—一般力学与力学基础]