## 3 Experimental Setup for Wire Rope Vibration Measurement under Tension  
The widely used 19 \(\times\) 7 construction wire rope was selected to investigate the vibration dynamic characteristics under tension. The wire rope was composed of steel, and it had a diameter of 8 mm, a length of 200 mm, a cross section of 29.70 mm\({}^{2}\), a mass per length of 0.27 kg/m, and an elastic modulus of 200 GPa. Figure 2 shows the structure of the wire rope used in the experiment. The wire rope had 19 strands, and each strand consisted of 7 wires. To investigate the effect of tension on the vibration of the wire rope, a static load was applied to the wire rope using a universal testing machine (RB301 UNITECH-M, R&B Co., Ltd., Daejeon, Republic of Korea). In order to compare with the wire rope structure, the dynamic characteristics of the steel beam were additionally investigated. The steel beam had a width of 30 mm, a thickness of 3 mm, a length of 200 mm, and an elastic modulus of 200 GPa. Figure 3 shows the experimental setup for the vibration measurement of the steel beam and wire rope under tensile test. They were supported by both jigs and excited by a small vibration shaker. The vibration was measured by the two accelerometers. For the steel beam, the vibration shaker and the accelerometers were attached at 2.4, 5.0, and 6.8 cm from the end, respectively. Tensions of 1, 2, 3, 4, and 5 kN were applied to the steel beam and wire rope. A Fourier transform analyzer (3560-B-030, B&K Inc., Brodhagen, ON, Canada) was used to measure the vibration transfer function with the tensions. functions was attributed to the change in bending stiffness. The vibration transfer function of the specimens under tension was affected by tension and bending stiffness factors. Figure 6 shows the vibration transfer function of the steel beam and wire rope with tensions. The transfer functions of the steel beam and wire rope were measured in the frequency ranges of 400-2000 and 200-2000 Hz. As the tension increased, the transfer function of the steel beam and wire rope shifted to the right. It was influenced by changes in the tension and bending stiffness. The wavenumbers with frequency were measured from the transfer function method. Figure 7 shows the measured wavenumbers of the steel beam and wire rope under various tensions. There were two wavenumbers, \(M\) and \(N\), in the specimens due to tension. The harmonic wave's wavenumber, \(\hat{M}\), held greater significance compared to the non-harmonic wave's wavenumber, \(\hat{N}\). The investigation was focused on the harmonic wave's wavenumber, \(M\). As the frequency increased, the values of the wavenumbers showed a tendency to increase. As the tension increased, the values of the wavenumbers \(M_{r}\) and \(M_{i}\) showed a clear tendency to decrease. Flexural wave speed \(c_{M}\) was calculated by dividing angular frequency \(\omega\) by the wavenumber \(M_{r}\), as represented by \(c_{M}=\omega/M_{r}\). Figure 8 shows the measured flexural wave speed of the steel beam and wire rope with tensions. The flexural wave speed was dependent on the frequency. As the frequency increased, the values of the flexural wave speed showed a tendency to increase. As tension increased, the flexural wave speed increased in both solid beam and wire rope structures. Figure 4: Measured and predicted transfer functions without tension of the steel beam in the frequency range of 400–2000 Hz. The transfer functions were used to calculate the translational and rotational spring stiffness of the joint between the specimen and the jig. Figure 5: Measured and predicted transfer functions of the wire rope with tensions in the frequency range of 200–2000 Hz. Figure 6: Vibration transfer functions of (**a**) steel beam and (**b**) wire rope with tensions. As the tension increased, the transfer function shifted to the right. It was influenced by changes in the tension and bending stiffness. Figure 7: Measured complex wavenumbers of a (**a,b**) steel beam and (**c,d**) wire rope with tensions.