# Numerical and Experimental Investigation of Guided Wave Propagation in a Multi-Wire Cable
## 5 Conclusions and Outlook  
In this study, an initial theoretical analysis of UGWs in a two-contact-wire system and an ACSR cable was completed from various perspectives. A time-transient FE numerical simulation and experimental study were conducted to validate the dispersion and wave structure properties, the contact acoustic nonlinearity effect, and the energy transfer model of multilayer wires. The main findings are summarized as follows:  
1. For the wave structures of the fundamental order longitudinal and flexural modes (i.e., L(0,1) and F(1,1)) in a 7-mm-diameter steel wire, the radial vibration displacements decreased but the axial vibration displacements increased with increasing radius. This trend became apparent with the increase in guided wave frequency below 200 kHz. The severity of dispersion and number of modes in a cylindrical structure were related to the bandwidth of excitation signals and the direction of excitation loads, respectively.
2. Guided waves with frequency \(f\) were excited to one of the two mechanically coupled wires. Received waves with frequency \(2f\) were observed in both wires due to the CAN effect at the contact interface. Numerical and experimental verification were performed using a monokinetic Hann-windowed sinusoidal excitation. There are many different wave modes simultaneously propagating in a multi-wire structure with different velocities at different frequencies, which could be predicted by dispersion curves. However, it is ineffective for dispersion curves to analyze the frequency behaviors of the wave signals of a certain mode, which could be analyzed using the CAN effect.
3. A minimally computationally expensive energy transfer model was used to predict the wave energy distribution in the wires located in different layers of the multi-wire cable. The approach was applied to analyze a pair of mechanically coupled wires using transient FE simulation. The acceleration data of the two wires were fitted to the model. The same investigation was experimentally performed on a 1.6-m-long 55-wire ACSR cable, and the wave energy of each layer was found to be consistent with the numerical analysis. Uniform distribution of the wave energy in each layer of a multi-wire cable is a basic requirement of SHM using a guided wave. The uniformity of the UGW energy depends on the contact between adjacent layers, which can be predicted by the model, when using piezoelectric transducers installed on the outermost layer of the cable. The model also could be used to optimize the excitation power of transducers and determine the effective monitoring range of SHM. In industrial applications, the results of this study could be used to improve the detection rate of the defects of wires located in the inner layers of the cable with low signal amplitudes, which are caused by the nonuniform wave energy distribution in different layers of the cable.  
For future research, we plan to study the UGW propagation in multi-wire cables using more precise contact and friction models to provide guidance for the guided wave inspection of cables, and the relationship between cable force and the CAN effect.  
[PERSON] and [PERSON] conceived and designed the models and methods presented; [PERSON] developed the experimental software tools; [PERSON] and [PERSON] helped in conception and experiments; [PERSON] helped in the simulations; [PERSON] performed the experiments and analyzed the data; and [PERSON] wrote this paper.  
This research was funded by the National Natural Science Foundation of China (Grant No. 61271084 and No. U1709216), the Science and Technique Plans of Zhejiang Province (Grant No. 2017C01042), the National Key Research and Development Program of China (Grant No. 2018 YFC0809000), and the Project of Inner Mongolia Power Group (Grant No. 20184733). And The APC was funded by the National Natural Science Foundation of China.  
The authors declare no conflict of interest.