In this study, the coupled ordinary differential equations for the galloping of the first two modes in iced bundled conductors, including in-plane, out-of-plane, and torsional directions, are derived. Furthermore, through numerical analysis, the critical conditions of this modal galloping are determined in the range of wind speed-sag parameters, and the galloping patterns and variation laws in different parameter spaces are analyzed. The parameter space is then divided into five regions according to the different galloping modes. Under the multimodal coupling mechanism of galloping, the impact of single and two kinds of coupled mode galloping on the spatial nonlinear behavior is explored. The results reveal that the system exhibits an elliptical orbit motion during single mode galloping, while an "8" motion pattern emerges during coupled mode galloping. Moreover, two patterns of "8" motion are displayed under different parameter spaces. This research provides a theoretical foundation for the design of transmission lines.
Keywords: galloping behavior; iced conductors; multimodal coupling; nonlinear vibration.