考虑弹性边界条件曲梁模型的覆冰输电线舞动

基于传统索单元理论的覆冰输电线舞动模型不能考虑平动和扭转的耦合作用以及扭转非线性。考虑绝缘子串和相邻跨度的刚度的影响，基于曲梁理论，根据Hamilton原理和Galerkin方法推导了考虑边界条件的三自由度舞动模型。采用Mathematica编制了曲梁理论模型和索理论模型程序分别对覆冰输电线舞动方程进行求解。算例分析表明，考虑边界条件的三自由度舞动曲梁理论模型与实测结果吻合较好，与索理论模型相比更优越。随着边界弹簧刚度的增大，竖向位移和侧向位移幅值随之增大，扭转位移幅值相应减小；发生舞动的下临界风速和上临界风速都在增大，舞动范围变小。弹性边界对副法向和扭转向模态影响较小，对轴向、竖向模态影响显著。

Galloping Curved-Beam Model of the Iced Transmission Line Considering Elastic Boundary Conditions

The galloping models of the iced transmission line based on the conventional cable theory cannot consider the translational and torsional coupling and torsional nonlinearity. According to Hamiton principle and Galerkin method, a 3-DOF galloping curved-beam model of the iced transmission line considering stiffness of insulator strings and adjacent spans as boundary conditions is formulated based on the curved-beam theory. The program code of galloping model based on Curved-beam and cable model developed by Mathematica is used to solve galloping equation of iced transmission line. An example analysis shows that the 3-DOF galloping curved-beam model of the iced transmission line considering elastic boundary conditions is in best agreement with experimental results, which has higher accuracy than the models based on cable theory among all models. With the increase of the boundary spring stiffness, vertical and horizontal displacement amplitudes raise and rotational displacement amplitude diminish accordingly. Both the critical wind velocity and supercritical wind speed for galloping increase. Simultaneously, the range of the wind speed for galloping becomes smaller. The boundary stiffness has a slight effect on horizontal and rotational mode functions and has significant influence on vertical and longitudinal mode functions.