Forced-self-excited system of iced transmission lines under planar harmonic excitations

This work involved analyzing the self-excited and forced vibrations of iced transmission lines. By introducing an external excitation load, the effect of dynamic wind on nonlinear vibration equations was reflected by the vertical aerodynamic force. The approximate analytic solution of the non-resonance of the forced-self-excited system was obtained using the multiple scale method. With an increase in excitation amplitude, the nonlinearity of the system was enhanced, and the forced-self-excited system experienced three vibration stages—namely, self-excited vibration, the superposition forms of self-excited and forced vibrations, and forced vibration controlled by nonlinear damping. Among these, the accuracy of the approximate analytic solution decreased with increase in nonlinear strength variations. When the excitation amplitude was greater than the critical value, the quenching phenomenon appeared in the forced-self-excited system, and the discriminant formula was derived in this work. In addition, the third-order Galerkin method, which considered the small sag effect, was used to discretize the nonlinear galloping governing equation. The response (principal resonance, harmonic resonance) of the forced-self-excited system was analyzed by time history displacement curves and phase diagrams. The conclusions of this work may contribute to the practical engineering of iced transmission lines. More importantly, as a combination of the Duffing equation and Rayleigh equation, the forced-self-excited system may have high theoretical research value.