三自由度体系覆冰导线舞动激发机理分析的矩阵摄动法

Matrix perturbation method for analysis of 3 DOF iced transmission line galloping mechanism

应用矩阵摄动法推导了三自由度体系覆冰输电导线离散自振频率下特征值实部一阶摄动解,在此基础上分析了舞动机理。相较于Den Hartog和Nigol机理所得到特征值实部单自由度解,一阶摄动解将分别多出一或二个附加项。由特征值实部摄动解结合模态振型可划分三种舞动激发类型。通过简化分析表明,当附加项主要对竖向起作用时,可将气动力类型分成六类用以分析附加项作用。以JD型六分裂覆冰导线为例,对Den Hartog系数均为负值的两类不同气动力类型下舞动激发特性进行了分析。结果表明,摄动解能较好反应实部真实变化。对于一、二类气动力,当附加项足够大时,舞动激发特性将表现出与按照Den Hartog机理所得完全不同的结果;与此同时亦将由于扭转气动力导数正负号的不同而产生巨大差异。

A three degree-oLfreedom lumped model of iced transmission line conductors with discrete frequencies subjected to galloping is analyzed. Through a matrix perturbation method,the approximate analytical solution of the eigenvalue real parts is determined. Different from the expressions by Den Hartog and Nigol mechanism, there comes one or two additional terms. Galloping mechanisms are then discussed based on the eigenvalue solutions and are grouped according to their modal shapes into three classes. Aerodynamic forces can be classified into 6 types when additional terms mainly affect the vertical real part. Take JD-6 iced bundle conductors for example, the perturbation solution has a satisfactory precision in comparison with numerical resuits. For the first two types with a negative Den Hartog coefficient, galloping excitation characteristics can be totally different compared with analyses according to the Den Hartog mechanism when the additional terms are large enough; meanwhile, galloping also differs a lot depend on the plus or minus characteristic of derivation of the torsional aerodynamic coefficient.