Singularity and chaos of nonlinear galloping for an iced transmission line

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Journal of Vibration and Shock ›› 2015, Vol. 34 ›› Issue (13) : 36-41.

HUO Bing1,2 LIU Xi-jun 1,2 ZHANG Su-xia 1,2 LIU Peng1,2

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Abstract

A three degree-of-freedom continuous dynamic model for an iced transmission line is proposed for describing the coupling of in-plane, out-of-plane and torsional vibrations, which is built on the basis of Hamilton principle with the consideration of geometric and aerodynamic nonlinearities. Galerkin procedure is applied to spatially disperse the partial differential governing equations. Together with average method, the bifurcation equation is derived from the average equations. The relevance of the bifurcated, unfolding and physical parameters is established, in which the bifurcated and unfolding parameters are separated and decoupled. Transition sets and their corresponding regions of original physical parameters are then made on the bifurcation equation by employing the singularity theory. The topological structures of bifurcated curves in different regions are presented, where saddle nodes and jumping phenomenon are found in certain regions. Numerical procedures are then implemented in the stable and jumping regions, respectively. The bifurcated diagrams obtained by numerical calculations are consistent with those derived by theoretical analysis, where periodic and chaotic solutions are observed, providing theoretical support to practical engineering.

Key words

Key words: nonlinear vibration / iced conductor / galloping / singularity theory / chaos

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HUO Bing1,2 LIU Xi-jun 1,2 ZHANG Su-xia 1,2 LIU Peng1,2 . Singularity and chaos of nonlinear galloping for an iced transmission line[J]. Journal of Vibration and Shock, 2015, 34(13): 36-41

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