Non-linear discrete models for the stochastic analysis of cables in turbulent wind

The random oscillations of small-sag, small-diameter cables induced by a turbulent wind are investigated through a reduced-order model containing both mechanical and aerodynamic non-linearities. The model is formulated on the basis of a state-of-the-art cable non-linear theory for the description of the mechanical behaviour, and of the quasi-steady assumption for the description of the aerodynamic forces. The discretization is carried out by a standard Galerkin approach and the resulting model is presented adopting a compact vectorial formalism enabling the formulation of expressions independent of the order of discretization as well as of the order of the non-linearities retained in the expression of aerodynamic forces. A Monte Carlo parametric analysis on a case-study, representative of a suspended cable typical of overhead power-line applications, introduces a discussion on the convergence of the modal expansions and highlights the respective importance of the different classes of non-linear terms included in the model.