In-plane free vibrations of multi-span transmission lines

Abstract

A theoretical method of in-plane mode and natural frequency of multi-span transmission lines is presented. The main idea is to establish moment balance equations of each insulator string and in-plane vertical motion equation of each span in multi-span section when the effect of conductor inertia component parallel to the chord on the additional horizontal tension of conductor is considered. The validity of theoretical mode and natural frequency is demonstrated by consistency with the numerical results of a typical five-span transmission line based on ABAQUS. It is shown that the mode of the five-span transmission line with a larger elasto-geometrical parameter exhibits asymmetrical shape that differed from those of single-span conductor. Considering the complexity of the theoretical expression, a simplified theoretical formulation of the modes and natural frequencies of multi-span transmission lines is obtained. Based on the curve of the frequency changing with the elasto-geometrical parameter, the various internal resonance conditions are discussed.