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Volume 10, Number 4, 2020, Pages 1355-1374                                                                DOI:10.11948/20190202
Limit cycle bifurcations in the in-plane galloping of iced transmission line
Peng Liu,Anqi Zhou,Bing Huo,Xijun Liu
Keywords:Galloping, limit cycle, bifurcation, Melnikov function.
      In this paper, we establish a mathematical model to describe in-plane galloping of iced transmission line with geometrical and aerodynamical nonlinearities using Hamilton principle. After Galerkin Discretization, we get a two-dimensional ordinary differential equations system, further, a near Hamiltonian system is obtained by rescaling. By calculating the coefficients of the first order Melnikov function or the Abelian integral of the near-Hamiltonian system, the number of limit cycles and their locations are obtained. We demonstrate that this model can have at least 3 limit cycles in some wind velocity. Moreover, some numerical simulations are conducted to verify the theoretical results.
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