# Numerical and Experimental Investigation of Guided Wave Propagation in a Multi-Wire Cable
## 1 Introduction  
Multi-wire cables play an important role as the main structural components in such mechanical and civil engineering applications as load carriers in elevators, lifting machinery, and cable-stayed and suspension bridges; post-tensioners in civil structures; and as overhead transmission lines (OVTLs) in power grids. Nondestructive inspection and structural health monitoring (SHM) of these cables are crucial to ensure the proper structural performance of cable-stayed and suspension bridges and high-voltage transmission towers. Bridge cables consist of multi-layer steel wires arranged in parallel within an equilateral hexagon and a polyethylene sheath wrapped around the wire bundle. Aluminum conductor steel-reinforced (ACSR) cables are the main components of the OVTLs between the transmission towers. Many nondestructive testing methods are available, such as visual inspection [1; 2], radiography [3], computed tomography [4], acoustic emission monitoring [5], ultrasound [1; 6], and magnetic flux leakage [7]. However, many of these methods have limitations when applied to multi-wire cables. For instance, conventional ultrasonic testing methods are impracticable for detecting large and longstructures, such as multi-wire cables, owing to the deficiency of local detection. Ultrasonic guided wave (UGW)-based nondestructive testing (NDT) techniques are increasingly being used to inspect various multi-wire cables given their high sensitivity, long-range inspection, and full cross-sectional coverage properties. Many studies [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18] related to guided wave dispersion properties, propagation characterization, signal processing methods, and wire breakage detection in multi-wire cables have been reported. When UGWs encounter the end or defect of a waveguide in propagation, reflected waves propagate along the original wave path and are received by the transducer, and the transmitted waves continue to propagate forward. Defect determination methods are used to measure the size and location of the defect, and evaluate the structural health state. The cross-section of the waveguide confines UGWs to propagate in only the length direction. However, the dispersive and multimodal nature of UGW propagation has to be analyzed. UGWs with a narrow frequency bandwidth often consist of several superposed modes with different wave structures [19] and propagation velocities. Therefore, the appropriate signal processing method is needed to analyze the acquired signals of received waves [20]. Multi-wire cables are composed of a number of parallel (e.g., bridge cable) or twisted (e.g., steel wire strands, ACSR cable) wires. The factors of helical and twisted geometry, tension state, and contact and friction stresses between adjacent wires complicate the numerical models of multi-wire structures [21]. Cables are commonly composed of a number of twisted wires with different diameters and materials, resulting in different wave velocities even at the same center excitation frequency. The contact condition between adjacent wires contributes to the complexity of the dispersion and propagation characteristics of the multi-wire structures. The factors of a large number of wires, a small diameter of an individual wire, and long length present challenges to the numerical modeling of guided waves propagation in multi-wire cables, such as slow convergence and time-consuming computation. The cable sheathing and irregular wire bundle surface geometry also make it difficult to design a transducer with high coupling efficiency, which is a critical part in industrial applications in the field. The overall dispersion characteristics of a multi-wire system with consideration of the contact stress between adjacent wires have been studied using a double-rod model, in which the guided wave mode conversion phenomenon was verified [22]. The dispersion curves could display the propagation velocities of all possible guided wave modes at different frequencies in a structure.