覆冰导线舞动的非线性动力学及参数分析

Nonlinear dynamics and parametric analysis for galloping response of iced conductor

为考察系统参数对覆冰输电线路舞动稳定性和动力响应的作用机制,基于Langrange方程,建立了考虑竖直向、水平向和扭转向三维非线性耦合效应的连续体分裂导线舞动模型。运用Rourh-Hurwitz判据准则在参数空间中标识了线路失稳时的临界条件,分析了不同阶主导振型作用下系统的稳定域及非稳定域。通过将系统参数视为状态变量的方式把原含参系统转化为不含参数的高阶扩张系统,应用不经中心流形定理降维的规范形理论推导了系统在临界点附近的Hopf分岔方程,并结合数值模拟方法检验了系统稳定条件和舞动响应理论解的准确性。在此基础上,讨论了不同主导振型作用下输电线路舞动响应随系统参数的变化规律。研究结果表明:初始攻角、来流风速和阻尼比等参数对覆冰导线稳定性与非线性分岔行为均有着重要影响。

To investigate the mechanism of stability and nonlinear dynamic response for iced bundled-conductor,a threedimensional galloping model,in which non-linear coupling effects in vertical,horizontal and torsional direction are considered,is proposed based on Langrange equation. By applying Routh-Hurwitz stability criterion,the galloping critical condition of iced transmission line is derived in the parametric space,and then the stable and unstable regions of system are studied,respectively,with different dominant modes. By regarding system parameters as state variables,the original system with varied parameters may be converted to an high-order extension system without parameters.Subsequently,the Hopf bifurcation equation at the critical equilibrium point is deduced by normal form theory without applying dimension reduction of center manifold. Furthermore,the critical condition of stability and analytical solution of galloping response are verified by numerical simulation. On this basis,the galloping responses in different dominant modes varied with parameters are discussed. The results show that some system parameters,such as initial attack angle,wind velocity and damping ratio,have significant effects on stability and nonlinear bifurcation behavior of iced transmission line.