Hysteresis Phenomenon in the Galloping of the D-Shape Iced Conductor

It is well known that there is a hysteresis phenomenon in the amplitude variation in the iced conductor galloping with the wind velocity, which will have more obvious disadvantages to the overhead transmission lines. But hysteresis characteristics in the conductor galloping have not received much attention. In this paper, a continuum model of the conductor galloping with D-shape ice is derived by using Hamilton principle, where the initial deformation, the geometric nonlinearity caused by the large deformation, and the aerodynamic nonlinearity are considered. The aerodynamic forces are described by using the quasi steady hypothesis, where the aerodynamic coefficients are expanded by the polynomial curves with a third order and a ninth order, respectively. The hysteresis phenomenon is analyzed by using the approximate solutions of the Galerkin discretized equation derived from the continuum model by means of the harmonic balance method. The influence of the different factors, dynamic angle of attack, span length, initial tension, and conductor mass, is obtained in different galloping instability intervals. And two important aspects about the point of the hysteresis phenomenon onset and the size of the hysteresis region over the wind velocities are analyzed under different conditions.