The Dynamics Study Of The Galloping Of Iced Bundle Conductors

The galloping of the long-span iced conductors is a research topic which is extensively concerned by the researchers all over the world. The large-amplitude galloping of the bundle conductors under the wind-excitation which is caused by interaction of liquid and solid, is a kind of complicated fluid-solid coupled motion. At the present time, many researchers adopt a discrete theoretical model or the finite element method in the research of the galloping of conductors, but in which the vibration characteristics of the conductors can not be globally embodied. In this paper, to represent the continuum characteristics of the conductors, using the aeroelasticity theory and nonlinear theory, a two-dimensional continuum model of the bundle conductors was established, which includes the motions of in-plane and out-of-plane. The research of the multiple order modes of this galloping model was analyzed both analytically and numerically. The main research contents and results in this paper are as follows.(1) Considering of the large cable sag effect, the deflection curve of the conductors in the static state was obtained by force analysis. According to the principle of elasticity mechanics, a two-dimensional coupled continuum model of the conductors can be established. By Galerkin method, a set of partial differential equations are transformed into a set of ordinary differential equations which are solvable. By making the first modal truncation of the equations, the two-dimensional coupled vibration equations were obtained. Using the data of wind tunnel tests, the fitting curve of the aerodynamic forces on in-plane and out-of-plane can be gotten, thus the aerodynamic model of the iced conductors was established.(2) Analytic solutions on the first mode of in-plane vibration equations and the first mode of in-plane and out-of-plane coupled equations were conducted respectively. The first order approximate solutions of the equations were obtained by the method of multiple scales, and the stable amplitudes of the first mode of in-plane and out-of-plane were achieved. The analytic solution confirms that the galloping of the conductors is dominated by the galloping of in-plane, and the galloping of out-of-plane is very minimal. The bifurcation equation was obtained from the in-plane average equation of conductors. The bifurcation diagram of the in-plane galloping under the small disturbance was analyzed by the singularity theory.(3) Furthermore, the analytical analysis of the first and second in-plane vibration modes has been made. The first and second modes coupled nonlinear dynamical equations of in-plane vibration were obtained by Galerkin method. The analytical analysis of the vibration condition of the first and second modes was done by the method of multiple scales.(4) The numerical analysis of the in-plane vibration equation of the iced conductors was conducted, and the phase diagram and time-domain curve were obtained, by which the validity of the analytical results was verified. The research of the effect of the aerodynamic parameters and structure parameters was calculated. The influence of the aerodynamic attack angle, damping ratio, and conductor tension on the amplitude and frequency of the vibration was analyzed. This may provide some theoretical basis which has guiding significance for the solution of the practical engineering problems.