# Numerical and Experimental Investigation of Guided Wave Propagation in a Multi-Wire Cable
## 1 Introduction
However, as for a UGW with a given mode and center excitation frequency propagating in a multi-wire structure, dispersion curves are incapable of predicting the change in frequency components of the wave signals due to the mechanical contact of adjacent wires. Studies of nonlinear guided waves used to detect microcracks in structures and to characterize materials have been reported [23; 24]. Higher-order harmonic waves were generated in the structure with microcracks when conducting the NDT inspection using an ultrasonic wave. Similarly, the contact acoustic nonlinearity (CAN) effect is also in existence in a contact multi-wire system. A longitudinal wave is excited in one rod of the two-contact-rod system, and harmonic waves with a frequency twice the excitation frequency are generated in both of the rods due to the CAN effect. Piezoelectric and magnetostrictive transducers have been widely used to excite and receive guided waves in a multi-wire cable. However, there is a nonmagnetostrictive effect in aluminum wires of an ACSR cable, and the magnetostriction of the innermost steel wires is too weak to generate guided waves due to the influence of the lift distance on the bias magnetic field caused by the layers of aluminum wires. Therefore, piezoelectric transducers, as practicable transducing devices, are commonly employed to carry out an inspection of an ACSR cable using UGWs. Several piezoelectric transducers, small in size, are uniformly installed on the outermost aluminum wires of the cable at the circumference [25]. The uniform coverage of the guided waves in the cable section relies on the contact between adjacent wires to transfer waves into inner layers from the outermost layer, where the transducers are installed. Models of the distribution and propagation of guided wave energy in different layers could provide guidance for determining the excitation power of transducers and estimating the monitoring range of the SHM system. In this paper, UGW propagation in a single cylindrical waveguide and double mechanically coupled cylindrical waveguides is introduced, including the dispersion properties and CAN effect. There are many different wave modes simultaneously propagating in a structure with different velocities at different frequencies or even the same frequency, which are partially caused by the dispersion phenomenon. However, the appearance of the high-order harmonic wave in the signal of a single mode wave with a single excitation frequency is caused by the CAN effect. An efficient energy-based model of coupled cylindrical waveguides is used to predict the wave energy distribution in wires located in different layers of an ACSR cable, by which the uniformity of the cross-sectional distribution of the guided wave could be obtained. Numerical transient finite element (FE) simulation and a two-dimensional (2D) fast Fourier transform were used to verify the results of the theoretical analysis. Experimental investigations were completed to generate and receive UGWs in a two-contact-wire cable and an ACSR cable with five-layer wires. The proposed numerical simulation models were fit to the experimental data.