Analytical and numerical approaches to nonlinear galloping of internally resonant suspended cables

A study is carried out on nonlinear multimodal galloping of suspended cables. A consistent model of a curved cable-beam, geometrically nonlinear and able to torque, recently formulated by the authors, is used. The model accounts for quasi-steady aerodynamic forces, including the effect of static swing of the cable and dynamic twist of the cross-section. Complementary solution methods are employed, namely, finite-difference and Galerkin spatial discretization, followed by numerical time-integration, or Galerkin spatial discretization in conjunction with Multiple Scale perturbation analysis. The different techniques are applied to a cable close to the first cross-over point, at which a number of internal resonances exist. Branches of periodic solutions and their stability are evaluated as functions of wind velocity. The existence of branches of quasi-periodic solutions, originating from narrow unstable intervals and propagating elsewhere, is also proved. Qualitative and quantitative results furnished by the different investigation tools are compared among them, and the importance of the various components of motion, accounted or neglected in the reduced models, is discussed.