Finite element modeling of cable galloping vibrations—Part I: Formulation of mechanical and aerodynamic co-rotational elements

Cables are widely used lightweight and efficient structural members affected by various nonlinearities. This paper is devoted to the development of a finite element approach to the study of the nonlinear dynamic behavior of cable structures under wind loading. Firstly, the formulation of a co-rotational beam-cable element is presented to account for cable geometrical nonlinearities within the context of an Updated Lagrangian approach. The Euler–Bernoulli kinematics is adopted in the co-rotated frame assuming small or moderate displacements and strains. Secondly, the formulation of an aerodynamic element, meant to be superimposed to the mechanical beam element, is developed to fully account for the nonlinearity of the aerodynamic forces. The wind interaction forces are computed within the framework of the quasi-steady theory. Appropriate procedures for applying the aforementioned elements in static and dynamic analyses are presented and applied to the study of the static configuration and the galloping vibrations of a suspended cable under steady and turbulent wind conditions. The results point out the importance of the first anti-symmetric in-plane mode on the galloping response of the iconic selected structure, and reveal the role of the mechanical and aerodynamic model by comparison with a different discretization based on cable finite elements. A mechanical model, such as the proposed co-rotational finite element formulation, which includes the description of torsional rotations is required to properly model the aerodynamic loads in dynamic galloping analyses under steady wind. The mechanical and aerodynamic assumptions, instead, play a less important role in the case of turbulent wind conditions, leading to an eminently buffeting response entailing a strong effect of the swing of the structure.