A new approach to the definition of self-damping for stranded cables

Aim of the paper is to propose a new approach for the determination of the so termed self-damping, or internal damping, of metallic cables. The formulation is developed starting from a recent mechanical model of a strand, from which the hysteretic bending behavior of stranded cables is derived. Each wire of the cable is individually modeled as an elastic curved thin rod. A kinematic model is defined to relate the axial strain and bending curvature of the strand to the generalized strains of the wire. The interaction among the wires belonging to adjacent layers is then studied by neglecting deformations of the contact surfaces and assuming a classic Amontons–Coulomb friction law. In the adopted strand mechanical model a function is derived, which defines the domain of admissible values of the wire axial force to prevent sliding. A simplified model of the cable hysteretic bending behavior is then derived from the cyclic response predicted with the adopted mechanical formulation of the strand, leading to a closed-form upper-bound estimate of the energy dissipated when the cable cross section is subjected to alternate bending. This expression is used as the starting block for the definition of an analytical equation giving an upper-bound estimate of the cable self-damping. The predictions of the proposed model are compared to available data resulting from experiments and empirical literature equations: the comparison is extended to a wide range of strands and parameters that characterize practically most of the configuration commonly used in overhead electrical lines.