Analysis of stability and modal interaction for multi-modal coupling galloping of iced transmission lines

Abstract

Considering geometric and aerodynamic nonlinearities, in this work, a reduced dynamic model with crescent-shaped ice accretions has been established to describe the coupling effects of in-plane, out-of-plane and torsional motions on galloping with longitudinal motions limited to in-plane and out-of-plane directions for simplification. Based on natural frequencies and associated eigenfunctions obtained for each of the three directions, motion equations containing two in-plane, two out-of-plane and two torsional components are obtained by Galerkin spatial discretization. By using eigenvalue analysis and numerical methods, galloping stability is investigated at different wind speeds, sags, initial wind attack angles, in-plane damping ratios and torsional damping ratios. The effect laws of different parameters on galloping are analyzed and Hopf bifurcation points are obtained, which denote the upper and lower critical wind speeds where the upper critical wind speed is mainly related to in-plane motion. Then, multi-modal interaction mechanisms with different parameters are discussed in detail. A variety of internal resonance behaviors are observed in the system and their similarities and differences are analyzed. Meanwhile, galloping presents synchronous and limited-amplitude characteristics, the reasons of which are explained. These reveal the occurrence of different energy exchanges among various modes. This research provides a theoretical foundation for the design of transmission lines.