The damping influence in monitoring the tension of cable using the vibration method

In the maintenance work of cable configurations, which have limitations such as cables in cable-stayed bridges, suspenders in suspension bridges, and hangers in arch bridges, tension on the cables is required. The safety of the cable is confirmed by checking whether the tensile force on the cable is within the allowable value. In the current widespread practice, cable tension is estimated using the vibration method by measuring the natural frequencies of the cable. However, this method is affected by several factors, including flexural rigidity, sag, and damper. The main difference is that natural frequencies (ω_n) are the theoretical frequency of vibration without any energy loss, while damped natural frequencies (ω_d) are of the actual system where damping (energy loss) is present. The undamped frequency is a system's inherent property based on its mass and stiffness, while the damped frequency is a practical measurement that is always less than the undamped frequency. This paper proposes a novel method for estimating tensile force that considers global damping. To model the cable as a Rayleigh beam, a theoretical equation for a viscoelastic system has been developed to estimate the natural frequency. The solution method calculates the cable tension and the material damping simultaneously from the natural frequencies. Previous studies verified the validity of the method. The maximum error in the tension is in the range of 4.71% in all valid tests. The evidence confirms the effectiveness of the proposed methods in tension estimation. In this research, the influence of damping on the evaluation of tension is investigated through analytical model, in which the natural frequencies, determined by the damping levels and the damped natural frequencies (measured frequencies). Then, the Hierarchical Bayes model was used to find stable estimates while preserving partial pooling, under sparse data, to stabilize estimates and fully quantify uncertainty. The results show that neglecting damping can cause noticeable errors, especially in low-tension or short cables. The study emphasizes the importance of considering damping in vibration-based tensile force assessments to enhance accuracy and reliability.