A Continuum Approach to the Nonlinear In-Plane Galloping of Shallow Flexible Cables

Abstract

The aeroelastic stability of horizontal, suspended, shallow, iced cables is studied via a continuum model. Both external and internal damping, consistent with the Rayleigh model, are taken into account. The quasi-static theory of the aerodynamic forces is applied. An in-plane nonlinear model of galloping is formulated, displaying the importance of internal damping, both on the critical velocity and on the limit-cycle amplitude. A perturbation procedure is developed for nonlinear analysis in nonresonant conditions (monomodal galloping). The modification of the galloping mode due to quadratic nonlinearities is studied, and its real or complex character is discussed.