Free vibration of transmission lines with multiple insulator strings using refined models

Abstract A theoretical dynamic model of two-span and three-span transmission lines with multiple insulator strings is presented. Unlike existing single-span models, the model has a considerable potential that the effect of the motion along the axial direction of transmission lines and insulator string swing on adjacent spans is considered. The equations of in-plane and out-plane motion of multi-span are set up by using a combination of moment equilibrium of insulator string swing and free vibration equation of each span, in which the longitudinal component of inertia is considered due to a motion of the support. Accurate and approximate solutions for the equations governing multi-span vibrations under self-weight are achieved with the continuity conditions of the displacement and force. Based on the theoretical formulas, a rich variety of symmetrical and asymmetrical modal features of adjacent spans interaction occurring in various parameters of transmission lines are discussed. The results show that the natural frequencies of corresponding in-plane and out-plane modes are heavily dependent on span number, the ratio of span lengths, Irvine's parameter λ and insulator string length. Furthermore, the finite element results based on the ABAQUS are reported, which establish the validity of the theory.