# Numerical and Experimental Investigation of Guided Wave Propagation in a Multi-Wire Cable
## 4 Experimental Analysis
### Overhead Transmission Line  
As described in Section 4.1, the third experimental sample LGJ-400/500 ACSR cable consisted of five layers (1-6-10-16-22) of wires composed of steel and aluminum. The innermost two layers were 7.5-mm-diameter seven-wire steel strands (1-6). Since the diameter of the single steel wire (\(D\) = 2.5 mm) was much smaller than that of the transducer (\(D\) = 10 mm), the entire steel strands were treated as one layer. The exciting transducer was installed on the end face of the strands' end. The receiving transducers were installed on the lateral faces of four layers (7-10-16-22) of another cable end, as shown in Figure 14a.  
Precise transient FE simulations that consider contact and friction stresses are computationally expensive. Applications of the FE method are limited to the multi-wire structures with short lengths and a smaller number of wires. For the sake of simplifying the description of UGW propagation behavior in multi-wire structures, such as bridge cables and ACSR cables, the energy-based model was used to investigate the experimental data. Guided wave signals recorded by transducers installed on each layer of the cable end (\(Z\) = 1.6 m) were processed by Matlab and are plotted in Figure 14b.  
In Figure 14b, the signals from the top to bottom were received by the transducers installed on the first, second, third, and fourth layers of the cable (from the inside to the outside). The wave packet marked by a circle in each signal was the direct wave excited by the exciting transducer. As a result of the contact and friction stresses between the adjacent wires in the same and adjacent layer, wave energy was transferred to each wire of the cable with the guided wave propagation. Each wire in  
Figure 14: Guided wave propagation experiments on the aluminum conductor steel-reinforced (ACSR) cable: (**a**) a photo of the exciting and receiving transducers installation, (**b**) the received time domain signals of each layer, and (**c**) the simulated and measured time average wave energy distribution in each layer.  
the inner layers of the cable was in contact with four adjacent wires: left wire, right wire, wire in the upper layer, and wire in the lower layer. Thus, the wave energy of each wire can be derived from Equation (1). The initial conditions in the equation were determined using a least squares fit with recorded signals. Since the active wire (first layer) was the steel strands in the center of the cable, the normalized wave energy of the wires in the same layer was equal (second, third, and fourth layers), as shown in Figure 14c. The measured wave energy can be obtained by integrating the received signal over the time domain:  
\[E(z)=\int_{t_{1}}^{t_{2}}U_{r}^{2}(z,t)\mathrm{d}t \tag{6}\]  
where \(t_{1}\) and \(t_{2}\) correspond to the time required by the fastest and slowest modes at the frequency of 60 kHz propagating from \(z=0\) to \(z=L\) (i.e., \(t_{1}=L/v_{group,fast}\) and \(t_{2}=L/v_{group,slow}\)), respectively, and \(U_{r}(z,t)\) is the radial vibration displacement at position \(z\). The fastest and slowest mode at 60 kHz frequency in the 3.2-mm-diameter aluminum wire group velocity dispersion curves shown in Figure 1b were the L(0,1) mode and the F(1,1) mode, respectively.