# An Omnidirectional Near-Field Comprehensive Damage Detection Method for Composite Structures
## 3 Experiments
### Calculation of Aviation Fuel Tank Wave Velocity  
Carbon fiber composite material is an anisotropic material. Therefore, the propagation speed of Lamb waves in different directions in a carbon fiber composite material is different. With the aim to identify the actual damage position in a composite material as accurately as possible, the propagation speed of Lamb waves in the oil tank was calculated first. As it is presented in Figure 6, the cross-array center position was in the right-angle coordinate system origin, and arrays I and II were along the \(x\)-axis and \(y\)-axis direction, respectively; there were twelve piezoelectric sensors which were arranged on the left and right side of the array, and they were numbered from 1 to 12. A cruciform, central-positioned piezoelectric element was used for excitation, and the remaining twelve piezoelectric elements acted as sensors. In Figure 6, the dotted-line arrows denote the excitation-sensing paths during the wave velocity measurement, and they were used to determine the velocity of Lamb waves in the plate at a certain angle. The propagation velocity of Lamb waves in the plate was obtained by using the active excitation-sensing method. The twelve piezoelectric sensing elements and the central piezoelectric element in the array corresponded to 12 excitation-sensing paths, and the propagation velocity in all the corresponding 12 different directions was calculated. Using the Shannon continuous complex wavelet transformation method, the start time of the excitation signal and the arrival time of each sensor-response signal were measured, and the difference between these two times denoted the propagation time of the Lamb wave. Since the distance of the piezoelectric sensors from the coordinate system origin was known, the propagation velocity of a Lamb wave in the tank could be calculated for each piezoelectric element in each direction using the corresponding wave propagation time. Figure 5: The experimental setup. (**a**) The experimental system (**b**) The cross-array and its numbered components. Figure 6: Schematic diagram of the piezoelectric sensor and energizing sensing channel. For instance, consider the piezoelectric sensor 4 (Figure 7) and the Lamb wave propagating in the 90\({}^{\circ}\)-direction. Using the first 2000 sample points and applying the Shannon continuous complex wavelet transformation method, we could calculate the starting time of the excitation signal and the arrival time of the sensing signal, respectively expressed as \(t_{0}\) and \(t_{4}\). The time difference between \(t_{0}\) and \(t_{4}\) denotes the time required by the Lamb wave to travel from the origin to the piezoelectric element 4, and it is given by:  
\[\Delta t_{4}=t_{0}-t_{4}=(1.835-0.5375)\times 10^{-4}=0.1298\ (\mathrm{ms}) \tag{10}\]  
According to the calculated propagation time, the propagation distance \(L_{4}\) was 200 mm. Therefore, the propagation velocity in the 90\({}^{\circ}\)-direction of a Lamb wave in the fuel tank of the carbon fiber composite material at the excitation of 50 KHz was calculated by:  
\[c(90^{\circ})=\frac{L_{4}}{\Delta t_{4}}=\frac{200}{0.1298}=1541\ (\mathrm{m/s}) \tag{11}\]  
Similarly, the propagation velocity of the Lamb waves in the other eleven directions was calculated. The propagation time in all directions was obtained by subtracting the arrival time of the excitation signal from the corresponding arrival time of the peak value of the Lamb wave, the A0 wave packet. Finally, the propagation speed of the Lamb waves in all directions was obtained using the wave propagation distance. The specific propagation velocity values are given in Table 1.  
Using the velocity values presented above, the velocity of the Lamb wave in the tank of a carbon fiber composite material at the excitation of 50 kHz in twelve directions was fitted to the propagation speed curve shown in Figure 8. Given the anisotropy and variable thickness of fuel tank structure, the reflection signal is more complex.