Energy-based dynamic damping identification in vibrating cables governed by hysteretic material behavior

The vibration of cables in both longitudinal and transverse directions, with or without an attached point mass, plays a key role in numerous industrial applications across a wide range of sectors. Although this problem appears simple and has been extensively investigated, several aspects of its dynamic behavior still require clarification. In particular, few studies explicitly relate local dissipative mechanisms at the material scale to the damping measured at the scale of the entire structure. In this article, two energy-based definitions of the damping ratio are derived analytically from material-scale dissipation, depending on the dominant deformation mode. Their relevance is assessed through a finite element model formulated within an explicit dynamic framework, accounting for geometric nonlinearities and for hysteretic material behavior via a visco-elasto-plastic constitutive law. Three configurations with different boundary and initial conditions are investigated, while focusing on responses dominated by the first vibration mode. The proposed energy-based damping measures are systematically compared with the structural damping ratio obtained from the logarithmic decrement. The close agreement observed between these approaches confirms the consistency of the proposed energy-based identification. A parametric study is then conducted to examine the influence of cable tension and added mass on the natural frequency and dynamic damping of the structure, in connection with stiffness and dissipation mechanisms identified at the material scale. Finally, the methodology is extended to the second vibration mode, thereby demonstrating its applicability beyond first-mode-dominated responses.