覆冰导线非线性舞动系统的奇异性和混沌分析  

Singularity and chaos of nonlinear galloping for an iced transmission line

作　　者：霍冰[1,2] 刘习军[1,2] 张素侠[1,2] 刘鹏[1,2] 

机构地区：[1]天津大学机械工程学院力学系,天津300072 [2]天津市非线性动力学与混沌控制重点实验室,天津300072

出　　处：《振动与冲击》2015年第13期36-41,47,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(51009107;51479136);天津市自然科学基金重点项目(13JCZDJC27100;09JCZDJC26800)

摘　　要：考虑几何非线性和气动载荷非线性,基于Hamilton原理建立了面内、面外和扭转三自由度耦合的连续动力学模型。借助Galerkin法对连续体模型进行空间离散得到系统的常微分方程。利用平均法解析求得系统的平均方程和分岔方程,建立了分岔参数、开折参数与工程参数的对应关系,并对分岔参数和开折参数进行解耦。根据奇异性理论得到关于工程参数的转迁集空间和各区域的拓扑结构,发现系统存在鞍结分岔点和跳跃现象。就理论解所得不同区域内典型的拓扑结构进行数值模拟,发现周期解与混沌解的存在,验证了理论解的正确性,同时为工程参数优化提供一定的理论支撑。A continuous dynamic model for an iced transmission line was proposed for describing the coupling of its in-plane,out-of-plane and torsional vibrations.It was built on the basis of Hamilton principle considering geometric and aerodynamic nonlinearities.Galerkin method was applied to spatially discrete the partial differential governing equations and acquire the oddinary differential equations of the line system.With the average method,the average equations and the bifurcation equation of the line system were deduced.The relationship between bifurcation parameters,unfolding parameters and physical ones was established,bifurcation parameters and unfolding ones were decoupled.Transition sets of the physical parameters and their topological structures in different regions were derived by employing the singularity theory.It was found that there exist saddle nodes and jumping phenomenon in the line system.Numerical simulations were implemented in stable and jumping regions,respectively.The bifurcation diagrams obtained with numerical simulations were consistent with those acquired with the theoretical analysis,the periodic and chaotic solutions were observed.The results provided a theoretical support for the optimization of the system’s physical parameters.

关 键 词：非线性振动 覆冰导线 舞动 奇异性理论 混沌 

分 类 号：TM726[电气工程—电力系统及自动化] O322[理学—一般力学与力学基础]