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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
      Considering the geometrical and aerodynamical nonlinearities, a model of in-plane galloping of iced transmission line is established 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 4 limit cycles in some wind velocity. Moreover, some numerical simulations are conducted to verify the theoretical results.