Abstract
A geometrically exact formulation of cables suffering axis stretching and flexural curvature is presented. The dynamical formulation is based on nonlinearly viscoelastic constitutive laws for the tension and bending moment with the additional constitutive nonlinearity accounting for the no‐compression condition. A continuation method, combined with a mixed finite‐difference spatial discretization, is then employed to path‐follow the static responses of cables subject to forces or support displacements. These computations, conducted in the quasistatic regime, are based on cables with linearly elastic material behaviors, whereas the nonlinearity is in the geometric stiffness terms and the no‐compression behavior. The finite‐difference results have been confirmed employing a weak formulation based on quadratic Lagrangian finite elements. The influence of the flexural stiffness on the nonlinear static responses is assessed comparing the results with those obtained for purely extensible cables. The properties of the frequencies of the linear normal modes of cables with flexural stiffness are also investigated and compared with those of purely extensible cables.
Highlights
Cables are used in a variety of engineering applications such as in suspension or cable-stayed bridges, power transmission lines, moorings in ocean engineering, or in aerospace deployable structures
A number of works have addressed the problem of modeling the flexural stiffness in cables, only a few works deal with nonlinear vibrations of general cables in lowtension regimes
A close agreement between the finite difference-based with number of grid points greater than or equal to 30 and finite element-based results has been found and it is such that only the outcomes of COMSOL are reported
Summary
Cables are used in a variety of engineering applications such as in suspension or cable-stayed bridges, power transmission lines, moorings in ocean engineering, or in aerospace deployable structures. Cables are effectively employed in long-span structures because they can be engineered and are light-weight structural elements with an outstanding stiffness in the axial direction and a significantly high strength. They do possess limitations due to the lack of out-of-plane stiffness and very light damping that make them often prone to large-amplitude. A number of works have addressed the problem of modeling the flexural stiffness in cables, only a few works deal with nonlinear vibrations of general cables in lowtension regimes. Wu et al 12–15 used a model of cables that includes the linear flexural stiffness contribution, and an approximate strain-displacement relationship for the elongation, to describe nonlinear vibrations of cables suffering loosening. Meaningful static responses of cables subject to various loading paths—support displacements or forces—are investigated in both cable models, here considered, the model with flexural stiffness and that without flexural resistance
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