覆冰导线非线性舞动系统的奇异性和混沌分析

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振动与冲击 ›› 2015, Vol. 34 ›› Issue (13) : 36-41.

论文

霍冰 1,2，刘习军 1,2，张素侠 1,2，刘鹏 1,2

作者信息 +

Singularity and chaos of nonlinear galloping for an iced transmission line

HUO Bing1,2 LIU Xi-jun 1,2 ZHANG Su-xia 1,2 LIU Peng1,2

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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，发现了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了一定的理论支撑。

Abstract

A three degree-of-freedom continuous dynamic model for an iced transmission line is proposed for describing the coupling of in-plane, out-of-plane and torsional vibrations, which is built on the basis of Hamilton principle with the consideration of geometric and aerodynamic nonlinearities. Galerkin procedure is applied to spatially disperse the partial differential governing equations. Together with average method, the bifurcation equation is derived from the average equations. The relevance of the bifurcated, unfolding and physical parameters is established, in which the bifurcated and unfolding parameters are separated and decoupled. Transition sets and their corresponding regions of original physical parameters are then made on the bifurcation equation by employing the singularity theory. The topological structures of bifurcated curves in different regions are presented, where saddle nodes and jumping phenomenon are found in certain regions. Numerical procedures are then implemented in the stable and jumping regions, respectively. The bifurcated diagrams obtained by numerical calculations are consistent with those derived by theoretical analysis, where periodic and chaotic solutions are observed, providing theoretical support to practical engineering.

导出引用

霍冰 1,2，刘习军 1,2，张素侠 1,2，刘鹏 1,2. 覆冰导线非线性舞动系统的奇异性和混沌分析[J]. 振动与冲击, 2015, 34(13): 36-41

HUO Bing1,2 LIU Xi-jun 1,2 ZHANG Su-xia 1,2 LIU Peng1,2 . Singularity and chaos of nonlinear galloping for an iced transmission line[J]. Journal of Vibration and Shock, 2015, 34(13): 36-41

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