## 1 Introduction  
A wire rope is a structure made by twisting several strands around a core. Each strand is composed of twisted steel wires. Wire ropes with high strength and flexibility are widely used in various industrial sites such as construction, shipbuilding, and manufacturing plants [1]. In particular, wire ropes are mainly used to move and support structures such as large suspension bridges, elevators, cranes, and cable cars [2]. Exposed to external shocks in their operational environment, wire ropes are susceptible to bending and vibration. Mitigating bending and vibration is crucial for maintaining the structural integrity of wire ropes and their connected structures. Bending stiffness and loss factor are important dynamic properties for evaluating resistance to bending and vibration damping. Because wire rope is subjected to various tensions, it is necessary to investigate its dynamic properties for various tensions. It is important to investigate the change in bending stiffness when a wire rope is bent or stretched. This change results from friction and relative movement among the wires. The bending stiffness changed with the slip between the wires [3]. When there was no slippage between the wires, they were glued and moved together. The wire rope behaved like a rigid beam, and it had the maximum bending stiffness. Additionally, the friction property of the wire rope was reduced due to no slippage between the wires [4]. The static friction between the wires was overcome, and the bending stiffness began to decrease as the wires slid. It had the lowest bending stiffness when all wires slid completely. When the wire rope transitioned from a loose state to a solid state, its moment of inertia increased [5]. The maximum bending stiffness appeared at high tension and low curvature [6]. The high tension made the wire rope more like a rigid beam, and the wires were glued together rather than sliding. As the tension was applied to the wire rope, a normal force was generated between the wires [7]. The sliding friction along the contact line between the wires was proportional to the normal force. Friction serves as an effective vibration damping mechanism, transforming kinetic energy into thermal energy. The friction due to relative motion between wires causes large damping. Scanning electron microscope micrographs were used to analyze individual wire wear in steel wire rope [8]. Frictional wear of the core wire was large, and the friction dissipated a large amount of energy. Most of the energy dissipation in the wire rope was caused by friction between the wires [9]. The damping was much greater in a wire rope, where friction could occur, than in a single wire. The steel wire rope degradation mechanisms and damage detection methods highlight the importance of understanding frictional interactions and wear in wire ropes [10]. Several studies have been developed to measure the vibration damping of wire ropes and their associated structures. The damping of a cable-stayed bridge model was measured using damped harmonic vibration caused by excitation with a hand-held shaker. The damping value for the main mode was calculated from the attenuation curves based on exponential curve fitting in the time domain [11]. The damping ratio of the stay cable was calculated through vibration modal analysis, and the vibration was measured using a video camera and a laser Doppler vibrometer [12]. The bending stiffness and vibration damping of the wire rope were investigated according to the applied static tension [13]. The damping ratio of each mode was calculated through modal parameter analysis in the frequency domain, and the damping ratio decreased as the tension increased. The bending stiffness and material damping were estimated based on the maximum a posteriori estimator with a frequency response function [14]. The effective bending stiffness of the cable was calculated based on the simply supported beam theory [15].