两分裂导线次档距振荡Hopf分岔研究
Studies on Hopf Bifurcation of Subspan Oscillation for Two Bundled Conductors

输电导线次档距振荡是风激振动的一种形式，严重影响输电线的安全稳定运行。针对两分裂导线次档距振荡现象，研究了两分裂导线次档距振荡系统的稳定性及其分岔现象。首先给出了两分裂导线次档距振荡的动力学方程，进而得到了系统的两个Hopf分岔点；然后利用中心流形定理将系统分别在两个Hopf分岔点降维，得到了两个Hopf分岔附近的极限环响应；最后应用后继函数法定性分析了两个Hopf分岔点的类别，所得结果与数值解吻合。
The subspan oscillation for transmission lines is one type of the wind-induced vibrations, which can lead to insecurity of transmission lines. In this paper, the stability and bifurcation of the subspan oscillation for two bundled conductors are investigated. Firstly, the governing equations and mathematical models of the subspan oscillation system are given, and two Hopf bifurcation points are obtained. Then central manifold theory is used to reduce the dimension of the subspan oscillation system, and limit cycle oscillations near these two Hopf bifurcation points are also obtained. Lastly, the successor function method is used to analyze types of the Hopf bifurcation points. All these results agree with the numerical analysis solution well