A full multispan two-degree-of-freedom (2-DOF) iced covered transmission line model is presented. Taking multispan conductors as the research object, based on the Hamiltonian principle, a nonlinear galloping model of multispan conductors considering the influence of insulator strings is established, and its galloping equation is derived. Based on the theoretical formula, the modes and frequencies in-plane and out-of-plane of the multispan conductor plane were obtained. After the partial differential equation was transformed into an ordinary differential equation by the Galerkin discrete method, the multiple scale method was used to solve the dynamic response of the multispan conductors. Through numerical calculations, this study is the first to systematically analyze the effects of parameters such as span number, span length, and tension on the in-plane and out-of-plane motion characteristics of multi-span conductors from a theoretical perspective. The research results in this paper have certain reference value for preventing multispan conductor galloping and interphase flashover.
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