一种新的覆冰导线舞动非线性有限元分析方法

本文基于Hamilton原理，建立了耦合三个平动自由度和一个扭转自由度以及偏心覆冰作用下导线的非线性舞动方程，提出了一种新的覆冰导线舞动分析非线性有限元模型，将相邻跨导线和绝缘子等效为线性弹簧单元，同时考虑覆冰导线非线性气动力和大幅舞动的几何非线性，采用Newmark-β时间积分结合修正的Newton-Raphson非线性迭代求解舞动有限元方程。本文数值解与D形覆冰导线舞动实测值无论在振幅还是频率方面均吻合得非常好，证明了本文新提出的导线舞动有限元模型的准确性。本文研究还表明：舞动是一种以上下运动为主的低频振动，通常发生在一阶上下自振频率附近，其振幅和频率由输电线路的物理参数和风载荷唯一确定，与初始运动状态无关。

A new nonlinear finite element analysis method on the galloping of iced conductors

Based on Hamilton’s principle, this paper formulates the nonlinear galloping equations of iced conductors, which couple three translational and one torsional degrees of freedom and involve the influence of eccentric icing. A new nonlinear finite element model of iced conductors in which the adjacent conductor spans and insulator strings are represented by linear springs is established here. Taking into account the nonlinear aerodynamic forces and the geometric nonlinearity caused by large amplitude galloping, the authors adopt the Newmark-β time integration algorithm in conjunction with modified Newton-Raphson nonlinear iteration strategy to solve those equations in finite element formulation. The numerical solutions of both amplitude and frequency obtained from the present method agree well with the measured values of the galloping of a D-shaped iced conductor, which proves that the current finite element model is accurate. The present research also indicates that the galloping is a kind of low-frequency vibration which mainly moves vertically and generally occurs around the first-order vertical natural frequency. The amplitudes and frequencies of the galloping are uniquely determined by the physical parameters of the transmission line and wind loads which are irrelevant to the initial state of the movements of the iced conductors.