In order to study the influence of dynamic wind on the nonlinear galloping characteristics of iced transmission lines, an external excitation load is added to the governing equation of iced transmission lines under the condition of stable wind, and a new forced self-excited system has been established. The frequency-amplitude relationship of the forced self-excited system under weak excitation and strong excitation is obtained by using the multiple-scale method. The principal resonances and superharmonic and subharmonic resonances of the forced self-excited system have also been analyzed. The results show that, in the forced self-excited system under strong excitation, when the excitation frequency is close to the integral and fractional times of the natural frequency, it is easier to produce 1/2-order subharmonic resonance, 2-order superharmonic resonance, and 3-order superharmonic resonance. In addition, numerical techniques provide bifurcation diagrams of different control parameters, which are able to highlight the effects of the simultaneous presence of the sources of excitation. When the control parameters (wind velocity, excitation amplitude, tuning parameter, tension, and Young’s modulus) change, the response amplitudes of the principal resonance and harmonic resonance will have multivalues, jump phenomenon, and hardening behavior. The control parameters can be used as a reference for engineering design. More importantly, as a combination of the Duffing equation and the Rayleigh equation, the forced self-excited system also has high theoretical research value.

中文翻译：

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强迫自激条件下输电线路的平面非线性舞动

为了研究动态风对冰输电线路非线性舞动特性的影响，在稳定风条件下，在冰输电线路的控制方程中增加了外部激励载荷，并建立了一个新的强迫自激系统。已确立的。利用多尺度方法，获得了弱激励和强激励下强迫自激系统的频率-振幅关系。还分析了强迫自激系统的主共振以及超谐波和亚谐波谐振。结果表明，在强激励下的强迫自激系统中，当激励频率接近自然频率的整数倍和分数倍时，更容易产生1/2阶次谐波谐振；2阶超谐谐振和3阶超谐谐振。另外，数值技术提供了不同控制参数的分叉图，它们能够突出激发源同时存在的影响。当控制参数（风速，励磁幅度，调整参数，张力和杨氏模量）发生变化时，主共振和谐波共振的响应振幅将具有多值，跳跃现象和硬化行为。控制参数可以用作工程设计的参考。更重要的是，作为Duffing方程和Rayleigh方程的组合，强制自激系统也具有较高的理论研究价值。数值技术提供了不同控制参数的分叉图，它们能够突出激发源同时存在的影响。当控制参数（风速，励磁幅度，调整参数，张力和杨氏模量）发生变化时，主共振和谐波共振的响应振幅将具有多值，跳跃现象和硬化行为。控制参数可以用作工程设计的参考。更重要的是，作为Duffing方程和Rayleigh方程的组合，强制自激系统也具有较高的理论研究价值。数值技术提供了不同控制参数的分叉图，它们能够突出激发源同时存在的影响。当控制参数（风速，励磁幅度，调整参数，张力和杨氏模量）发生变化时，主共振和谐波共振的响应振幅将具有多值，跳跃现象和硬化行为。控制参数可以用作工程设计的参考。更重要的是，作为Duffing方程和Rayleigh方程的组合，强制自激系统也具有较高的理论研究价值。励磁振幅，调谐参数，张力和杨氏模量）的变化，主共振和谐波共振的响应振幅将具有多值，跳跃现象和硬化行为。控制参数可以用作工程设计的参考。更重要的是，作为Duffing方程和Rayleigh方程的组合，强制自激系统也具有较高的理论研究价值。励磁振幅，调谐参数，张力和杨氏模量）的变化，主共振和谐波共振的响应振幅将具有多值，跳跃现象和硬化行为。控制参数可以用作工程设计的参考。更重要的是，作为Duffing方程和Rayleigh方程的组合，强制自激系统也具有较高的理论研究价值。