Piecewise-Fitted Formula for Cable Force Identification Considering Bending Stiffness, Sag, and Inclination

The identification of cable forces plays an important role in the construction, vibration control, and health monitoring of cable structures. In practice, cable vibrations are mainly affected by the coupling of bending stiffness, sag, inclination, and boundary conditions, so it is difficult to establish an explicit functional relationship between frequency and cable force through the vibration method for facilitating application to engineering. To overcome this difficulty, the explicit expression of the frequency of the cable considering bending stiffness, sag, and inclination is derived for the first time and a novel cable force identification method for determining the piecewise-fitted formula (PFF) according to the cable parameters is proposed. The paper first reviews the cable force identification formulas based on cable frequencies. Then, the theoretical analysis model and differential equation of cable vibration considering the aforementioned factors are established. Based on these derivations, the explicit general formula of cable force identification based on fundamental frequency is derived. Next, according to the cable parameters, the value ranges of two nondimensional parameters characterizing the bending stiffness and sag of cables are divided to fit the corresponding coefficients of the PFF. Finally, numerical simulation and experimental data show that the PFF is more accurate and applicable than the existing formulas. This method can be conveniently applied to the field detection and online monitoring of cable forces.