In the classic cable theory, vibration of cables is usually analysed by writing the equations of motion in the nearness of the initial equilibrium configuration. Thus, a fundamental difference exists between out-of-plane motion, which substantially corresponds to the linear behaviour of a taut string, and in-plane motion, where self weight determines a sagged initial profile. This work defines a continuous approach in order to establish the initial shape when the cable is subjected to wind or fluid flow arbitrarily directed and a finite element approach in order to investigate the dynamic around the initial equilibrium shape of the cable. In particular, the equations of motion for a three dimensional case are written fully accounting for initial shape. This means that in the additional deformation also in the out-of-plane and along cable directions there is a term linked with the initial position. Stochastic solutions in the frequency domain are derived for a wind-exposed cable after linearization of the problem and by applying the Proper Orthogonal Decomposition Technique (POD) with the aim of reducing computational effort. Differences are shown with respect to the case in which out-of-plane initial displacement is neglected. In addition, a POD based approach to simulate modal wind forces is proposed and applied to the fully nonlinear equations of motion.

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