Three‐Degree‐of‐Freedom Model for Galloping. Part II: Solutions

Abstract

Internal nonresonant and resonant galloping of an iced electrical transmission line is studied by employing a three‐degree‐of‐freedom (3DOF) model formulated in part I where the conditions for the initiation of galloping and the governing bifurcation equations were derived for dynamic motions. Perturbation techniques are employed so that the governing equations can be manipulated algebraically to obtain explicit expressions for the periodic and quasiperiodic solutions as well as their stability conditions. For the nonresonant case, sequent bifurcation solutions and stability boundaries show that secondary and tertiary bifurcations exist. It is also demonstrated that phase differences between different component movements do not affect the stability conditions for the nonresonant case even though they are significant for the resonant cases. Practical examples are presented to demonstrate the applicability of the theory. Results at different wind speeds indicate that a previously defined “smallness” parameter is appropriate for assessing the reliability of the solutions. Furthermore, a comparison of the results from simple models having various degrees of freedom suggests that it is advisable to employ at least 3DOF.