Stability Analysis For Wind-induced Vibration Of Eccentric Cables

Suspend cables are wildly used in cable bridges, membrane structures and transmission lines for its low weights, high strength and easy to construct. In the winter when the cable was covered by ice caused by the rain and snow, the eccentricity makes the in-plane and out-planes vibration couple with the torsion vibration. So the motions of the cable become much more complicated, and it maybe leads to some terrible results. In the spring of 2008 the ice-covered transmission lines fractured in the south of China which made lots of economic loss and large-scale power-failure. So it's necessary to investigate the nonlinear dynamics and the stable region of the eccentricity cables loaded by wind.The wind-induced vibration is considered to be the in-plane, out-plane and the torsion vibrations. The wind load is considered as a nonlinear function of the angle of attack, and Hamilton principal is used to obtain the governing partial differential equation of motion. Galerkin approach is adopted to reduce the governing partial differential equation to an approximate system with few numbers of DOFs. The stability conditions can be verified with numerical solutions. At the given point of Hopf bifurcation an approximation is used to get the stability region saving lots of time and workload. The research work can be summarized as follows:(1) A 3-degree-of-freedom eccentricity cable loaded by wind model is established. The wind load is considered as a nonlinear function of the angle of attack, and Hamilton principal was used to obtain the governing partial differential equation of motion. The Galerkin approach is adopted to reduce the governing partial differential equation to differential equations.(2) Analysis the differential equations, explicit conditions are provided for loss of stability based on the Routh-Hurwitz criterion while for generation of stable limit cycles Hopf bifurcation. The stability conditions can be verified with numerical solutions. Compare with the 2-degree-of-freedom model established in other papers; obtain the advantages of the model in the research.(3) According to the 3-degree-of-freedom model established in the paper, a cable element is built for the finite element discrimination. The mess matrix and the stiffness matrix are derived. A finite element program is used to solve the wind induced vibration of the eccentricity cable.