PSI - Issue 37

Reza Soleimanpour et al. / Procedia Structural Integrity 37 (2022) 956–963 6 Reza Soleimanpour, Sayed Mohamad Soleimani and Naser Khaled Mohammad / Structural Integrity Procedia 00 (2019) 000 – 000

961

Fig. a show the acquired data at the measurement locations in time-domain when the incident wave was excited at actuator and the data was measured at receiver 2. In addition to the calculated time-domain data, the data proceed in time-frequency domain for both linear and nonlinear guided waves is also shown in Fig. b and Fig. c respectively. According to the arrival time of the wave packages in Fig. a, the first, second and third wave packages attribute to the incident wave, linear reflected wave from the bolted joint and wave reflection from the beam end, respectively. As the linear reflected wave is slightly overlapped with the incident wave package, it is difficult to accurately determine the arrival time of the linear reflected wave without the baseline data. This is even more complicated for more complex structures or when defect is close to the receivers. However, the time domain data shows distortion in few wave packets as pointed out in Fig. a which was further investigated in time-frequency domain. The data was processed using methodology explained in methodology section. The wave packets travelling at incident wave frequency can be seen in Fig. b. The first contour attributes to the incident wave captured at the receiver whereas the other contours in the background attribute to the wave packets discussed in previous paragraph that arrive at the receiver later. The nonlinear wave packets travelling at double central frequency can be seen in Fig. c. As can be seen from this graph, there are several wave packets that travel at second harmonic frequency. However, these wave packets cannot be seen in Fig. b as they have smaller amplitude than that of linear waves. These two graphs are very useful as they reveal information regarding the wave packets and the time of arrival for each wave packet with central and second harmonic frequency. Based on Fig. c, several nonlinear wave packets arrive at sensor after arrival of the linear incident wave. The first contour with largest energy attributes to first reflected nonlinear wave from the loose bolted joint whereas the rest of contours with smaller energy attribute to the nonlinear waves generated due to interaction of reflected wave from the boundary with loose bolted joint or due to further clapping of defect interfaces. By looking at first contour in Fig. c and the second contour at Fig. b, it can be seen that the linear wave packets reflected from loose bolted joint are mixed the nonlinear wave packets. This explains the distortions observed in time domain graph in Fig. a. However, if the length of specimen is long enough, these two wave packets will separate at some point in specimen as they travel with different group velocities.