COUPLED VERTICAL AND HORIZONTAL GALLOPING

Galloping can occur when wind blows on ice-coated conductors. In this paper, the linearized coupled vertical-horizontal galloping equations are derived and the eigenvalues defining the motion are determined analytically. The intrinsic coupling between the vertical and horizontal equations requires that there be no vertical motion if the horizontal motion is constrained. Furthermore, vertical galloping may be initiated by a horizontal displacement or velocity. The solution of the eigenvalue equation indicates that the coupled galloping criterion may be either more or less stringent than Den Hartog's criterion. The galloping trajectory is either a straight line at a small angle to the vertical, or under more extreme conditions, defines an elliptical envelope. Solutions are obtained for four cases chosen from the literature to illustrate the effect of different combinations of values of the aerodynamic parameters.