考虑弹性边界曲梁模型的覆冰输电线舞动分析

MULTI-SCALE METHOD GALLOPING ANALYSIS OF ICED TRANSMISSION LINES BASED ON CURVED-BEAM MODEL CONSIDERING ELASTIC BOUNDARY CONDITIONS

采用解析法求解覆冰输电线考虑弹性边界的曲梁舞动模型有助于深入理解舞动发生机理。根据扭转向频率特性将三自由度舞动模型简化成更加适用于解析法求解的两自由度舞动模型,然后利用多尺度法分别推导出了1∶1和2∶1内共振情况下的简化幅值方程。接着考察了自由度缩减方法差异引起的轴向模态函数变化和弹性边界对舞动分岔和稳定、舞动幅值和临界风速的影响。结果显示,轴向模态函数的变化对1∶1内共振情况下分岔和稳定、舞动幅值和临界风速的影响较小,对2∶1内共振情况下相应值影响较大。当考虑截面偏心时,1∶1内共振条件下,弹性边界使发生不稳定舞动的风速范围减小。覆冰导线在弹性边界条件下的位移幅值相应减小,下临界风速增大,上临界风速相应减小,舞动风速范围减小。

An analytical approach to solving the galloping model for iced transmission lines based on curved-beam theory and considering elastic boundary condition was developed and can contribute to understanding the galloping mechanism. A two-degree-of-freedom galloping model is reduced from a three-degree-of-freedom galloping model according to the frequency characteristic of rotational direction, then the multi-scale method was used to deduce the 1:1 and 2:1 internal resonance simplified amplitude equations. Then, the effects of variation in the axial model function brought about by the difference between DOF reduction methods and the elastic boundary condition on bifurcation and stability, amplitudes, and galloping critical wind velocity were identified. Results indicate that the impact of variation of the axial model function on the galloping bifurcation and stability, galloping amplitudes and critical wind velocity is slight in the 1:1 internal resonance case and, for corresponding parameters, comparatively great in the 2:1 internal resonance case, especially when not considering the eccentricity of the cross-section. When considering the eccentricity of cross-section in the 1:1 internal resonance case, unstable galloping wind velocity ranges brought about by the elastic boundary condition decrease. The influences of the elastic boundary condition on the galloping amplitudes and critical wind velocity are distinctive; the corresponding displacement amplitudes of the iced transmission line and the supercritical wind velocity decrease, the critical wind velocity increases, and the galloping wind velocity range lessens under the elastic boundary condition.