Unified Practical Formulas for Vibration-Based Method of Cable Tension Estimation

Abstract

In this paper, unified practical formulas are proposed to estimate cable tension for vibrations under different boundaries. Correction coefficients are applied to the cable tensions calculated from the taut string theory. In these formulas, a dimensionless parameter η is introduced to represent the relative bending stiffness of the cable in lieu of the dimensionless parameter ξ in the previous formulas found in practice. Results have shown that the proposed formulas are accurate. For the fixed-fixed boundaries, the error in the estimated cable tensions for various frequencies is less than 3% for η ≤ 0.88, and less than 1% for η ≤ 0.55. For the fixed-hinged boundaries, the error in the estimated cable tensions for various frequencies is less than 1% for η ≤ 0.9. If there are multiple frequencies in the in-situ measurement, the proposed formulas can be used to identify the cable tension and bending stiffness simultaneously by solving a quadratic equation. The proposed formulas have been validated against several numerical examples as well as practical test cases.