Stability Analysis of Parametric Vibration in Overhead Conductors Under Time-Varying Tension

This paper investigates the impact of dynamic tension induced by adjacent span vibrations on the vibrational characteristics of overhead conductors. A simplified model is established, considering the overhead conductor with a symmetric structure as a simply supported flexible long wire subjected to axial time-varying tension at one end. The transverse motion partial differential equation of the overhead conductor under time-varying tension is formulated and discretized into a parametric vibration equation with time-varying coefficients using the Galerkin method. Based on Floquet theory, the study systematically analyzes the influence of time-varying tension on system stability, delineates the boundaries of parametric resonance instability regions, and conducts time-history analysis of vibrational responses within these regions. The research demonstrates that when the frequency of the time-varying tension approaches the line’s natural frequency or its double, the system is prone to instability. While the damping coefficient can enhance system stability, it has limited effectiveness in suppressing the primary instability region. The study found that the vibrational responses of parametric vibrations exhibit nearly symmetric distributions within the instability regions and along the critical boundaries. Adjusting the frequency differences between adjacent spans effectively mitigates the parametric resonance issues in overhead conductors, providing valuable insights for engineering design.