Cable Force Identification With Unknown and Variable Elastic Boundary Supports: Theory and Validation

The vibration method is widely used for identifying cable tension. However, the boundary conditions of cables in structures are often not ideally hinged, resulting in a significant error in identifying cable forces. To precisely determine the stress state of cables, this paper proposes a methodology for cable force identification with unknown and variable elastic boundary supports. First, an equivalent single-degree-of-freedom (SDOF) model of the cable with variable elastic boundary supports is established. A mathematical relationship between the frequencies of ideal hinged cables and those with elastic boundary supports is then established. Subsequently, the first-order frequency is modified by accounting for the mode shape values at the midpoint and both endpoints of the cable. Finally, a methodology for cable force identification with unknown and variable elastic boundary supports is proposed and validated through numerical simulations, experiments, and on-site tests. The results indicate that the proposed cable force identification method can adapt excellently to the variable elastic boundary supports without relying on known the boundary constraint stiffness. In numerical simulations, the identification errors of the proposed method are all less than 1%, while in experiments and on-site tests, the identification errors are within 5%, demonstrating its high accuracy and strong adaptability. The proposed method considers the complex boundary conditions of cables, eliminating the need to solve for unknown boundary constraint stiffness, indicating that it can adapt to the unknown and variable boundary stiffness of cables.