Measurement method of natural frequencies and tension forces for cables based on elasto-magnetic sensors calibrated by frequencies

Vibration-based (VB) method and elasto-magnetic (EM) method are usually used to measure cable forces of cable-supported bridges. For the VB method, it is difficult to accurately identify each order natural frequency of the cable disturbed by random excitations, and there are also no precise selection criteria between the taut string model and the hinged beam model. For the EM method, it is not convenient to calibrate EM sensors on bridges in service due to unknown cable forces. To address these issues, a vibration-based elasto-magnetic (VBEM) method is proposed. In this method, a numerical model describing the tie between each order natural frequency and induced voltage was constructed first, and then, a new cable force formula with nominal flexural stiffness was derived. To verify the VBEM method, a steel strand experimental platform was built and the load applied to the steel strand was achieved by a jack. At 18 °C, the first three order natural frequencies of the steel strand and corresponding induced voltage were recorded for each load. According to the obtained experimental data, the VBEM method is tested and analyzed. The results show that the VBEM method exhibits the ability to identify each order natural frequency of the steel strand with high precision; the introduction of nominal flexural stiffness makes the hinged beam model cover the taut string model, resulting in tension force measurement with satisfactory accuracy; the constructed models do not contain tension forces, and this will make it very beneficial to calibration of EM sensors on bridges in service.