Study on chaos in galloping of the transmission line

Galloping is one of the important causes to catastrophic accidents of transmission lines. This paper aims to investigate the motion patterns that may exist in the conductor galloping, especially the existence of chaotic motion. First, the two-degree-of-freedom differential equations of motion containing lateral and torsional are established by using Lagrange equation. Next, the equations are solved for 1:1, 2:1 and 3:1 resonance cases by using the multiple scales method and the corresponding averaged equations are obtained. Based on the amplitude solvable conditions, Arnold tongue curves are constructed in the Ω-U plane. According to Arnold tongue method, the Ω-U plane is divided into 6 regions on the basis of different overlapping cases among the three Arnold tongues. Finally, the motion patterns in the six parameter regions are studied by numerical experiments. Meanwhile, the chaotic motion is found when setting U=30.5 m/s and Ω=3.1781. It is an explanation of the chaotic motion that the three resonance patterns may coexist when certain parameters are chosen, and the mutual transformation of them leads to the complex motion patterns of the system.