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1. Introduction
It is well known that iced conductor galloping is a typical low-frequency self-excited vibration phenomenon [1]. Conductor galloping represents a classical motion instability mechanism in the steady flow over a noncircular cross-section caused by ice accretion on the conductor. This conductor motion is characterized by large amplitude (possibly > 10) and low frequency (approximately 0.1–3 Hz) [2]. Although conductor galloping trace has usually an elliptical orbit on field observations, the predominant motion in galloping is vertical. Galloping can cause various kinds of structural and electrical damages in overhead lines, which can have devastating economic and social consequences [3, 4].
Conductor galloping has been studied extensively over a half century since Den Hartog [5] firstly established the vertical galloping mechanism using the quasi steady hypothesis to describe the linearized aerodynamic forces based on a simple single degree-of-freedom (DOF) model. Whereafter Nigol and Buchan [6, 7] proposed a torsional galloping mechanism based on a two-DOFs model coupled with vertical and torsional oscillations. And Yu et al. [8, 9] obtained a torsional feedback mechanism using a three-DOFs model coupled with vertical, horizontal, and torsional oscillations. And later, with the development of linear and nonlinear motion instability theories, galloping phenomenon has been studied widely by using nonlinear vibration methods [10–14].
At present, the Den Hartog theory and the torsional theory are still the two important and dominant mechanisms to explain the phenomenon of conductor galloping. The torsional theory shows that the torsional motion has a considerable effect on the instability and that its coupling with the vertical motion is responsible for most cases of the conductor galloping phenomenon [15], which is the main difference with the Den Hartog theory. So it can be excited based on Den Hartog mechanism when the torsional motion does not occur in the process of conductor galloping. And if the torsional motion is observed, the conductor galloping...