## 3 Experimental Setup for Wire Rope Vibration Measurement under Tension
### Wire Rope Dynamic Characteristics Analysis under Tension  
The dynamic characteristics of the steel beam and wire rope were analyzed with tensions. The wavenumbers were used to measure the dynamic characteristics, including bending stiffness and loss factor. Figure 9 shows the measured dynamic characteristics of the steel beam and wire rope with tensions. The bending stiffness and loss factor of the wire rope showed relatively large changes as the tension increased compared to the steel beam. The moment of inertia was important because the bending stiffness was determined by an elastic modulus and the moment of inertia. The steel beam, being in a solid state, exhibited minimal changes in the moment of inertia as the tension increased. The bending stiffness of the wire rope showed a relatively greater change as the tension increased than that of the steel beam. On the other hand, as the applied tension on the wire rope increased, it transitioned from a loose state to a solid state, resulting in a significant increase in the moment of inertia. The loss factor of the steel beam remained relatively unaffected by the increase in tension, whereas the loss factor of the wire rope showed a noticeable decreasing trend. As the tension increased, the wire rope transitioned from a loose state to a solid state, and the adhesion between wires and strands increased. The relative displacement between the wires and strands was reduced due to the strong adhesion, which reduced slippage between them. As sliding did not occur, the friction of the wire rope was reduced. Because friction was associated with energy dissipation, a decrease in friction led to reduced vibration damping. Unlike the wire rope structure, the steel beam structure had a weaker relationship between tension and friction. Therefore, the tendency of vibration damping with increasing tension did not appear clearly. Figure 10 shows the hysteresis curves of the steel beam and wire rope. The area of the hysteresis curve expresses the energy dissipated by internal friction. A large area of the hysteresis curve indicates a large vibration damping and loss factor. The measured hysteresis curve areas of the steel beam and wire rope were 0.11 and 0.24 MPa, and the area of the wire rope was larger than that of the steel beam. This indicated that the wire rope had a higher vibration damping and loss factor than the steel beam. This supported that the wire rope, being in a relatively loose state compared to the steel beam, exhibited greater energy dissipation due to friction. Figure 11 shows the average dynamic characteristic values of the steel beam and wire rope with tensions. A regression model was created to estimate the bending stiffness and loss factor with tensions. In the model, R\({}^{2}\) was used to measure the correlation between the independent and dependent variables, and the \(p\)-value was determined to evaluate the statistical significance. To ensure statistical significance of the model, the \(p\)-value must be lower than 0.05 [23]. In the steel beam, the R\({}^{2}\) and \(p\)-value were 0.643 and 0.055 for the bending stiffness, and they were  
Figure 8: Measured flexural wave speed of a (**a**) steel beam and (**b**) wire rope with tensions. As the frequency increases, the values of the flexural wave speed show a tendency to increase. As tension increases, the flexural wave speed increases in both solid beam and wire rope structures. 0.012 and 0.837 for the loss factor. Therefore, the bending stiffness and loss factor of the steel beam structure did not have a clear correlation with tensile force. As shown in Figure 4, regardless of the change in dynamic characteristics, the transfer function shifted to the right due to the increase in tensile force. In the wire rope, the R\({}^{2}\) and _p_-value were 0.995 and 9.75 \(\times\) 10\({}^{-6}\) for the bending stiffness, and they were 0.990 and 3.66 \(\times\) 10\({}^{-5}\) for the loss factor. Therefore, the dynamic characteristics of the wire rope structure had a clear correlation with tensile force.