Three‐Degree‐of‐Freedom Model for Galloping. Part I: Formulation

Abstract

A three‐degree‐of‐freedom model is developed to comprehensively describe and predict different galloping behavior observed on a single iced, electrical transmission line. Interactions are accommodated between a line's plunge, twist, and swing in the along‐wind direction. Eccentricity of the cross section is also considered and the longitudinal static stiffnesses of adjacent spans are included. The initiating conditions for galloping are derived in closed form. For the parameters causing galloping, perturbation techniques are employed to derive the governing bifurcation equations under the assumption of a weak nonlinearity. A total of 10 (one nonresonant and nine internal resonant) plausible cases are considered. Two different time averaging approaches are used for different cases to simplify the algebra in deriving the explicit solutions. Aerodynamic effects are incorporated in the structural stiffness matrix to improve accuracy and to extend the range of application of the perturbation. A robust criterion is developed to assess the reliability of the solutions. Explicit periodic and quasiperiodic states and their stability conditions are computed in a companion paper.