Nonlinear galloping of internally resonant iced transmission lines considering eccentricity

Based on the curved-beam theory, a nonlinear galloping model considering three displacement (normal, bi-normal and tangential) components and twist is formulated. According to the property of transmission line, one reduced (normal and bi-normal) galloping model, with regard of bending, rotation and eccentricity of cross section, is obtained. Moreover, the initial rotation angle is also introduced in galloping and aerodynamic models. Additionally, based on the reduced model, the bifurcation and stability of the two cases (1:1 resonance and 2:1 resonance) are analyzed. The results turn out that the importance of ice eccentricity needs to be highlighted. Finally, multiple stabilities are found through the analyses of bifurcation and stability and proved by the reduced model and Reduced Amplitude Modulation Equations (RAME) numerically integrated in time history.

► We model the galloping of iced transmission line considering eccentricity.
► We analyze bifurcation and stability of 1:1 and 1:2 resonant cases.
► Ice Eccentricity has a great effect on bifurcation and stability.
► The phenomenon of multiple stabilities is found.
► The phenomenon of multiple stabilities is proved by the reduced model and RAME.