Limit cycle bifurcations in the in-plane galloping of iced transmission line |
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Authors: | Peng Liu Anqi Zhou Bing Huo and Xijun Liu |
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Institution: | Shanxi Key Laboratory of Material Strength & Structural Impact, Taiyuan University of Technology, 79 Yingze West Street, 030024 Taiyuan, China,Department of Mechanics, Tianjin University, 135 Yaguan Rd, 300356 Tianjin, China,College of Mechanical Engineering, Tianjin University of Science & Technology, 1038 Dagu South Rd, 300222 Tianjin, China and Department of Mechanics, Tianjin University, 135 Yaguan Rd, 300356 Tianjin, China |
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Abstract: | 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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Keywords: | Galloping limit cycle bifurcation Melnikov function |
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