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Observation of Lamb Wave Mode Conversion on an Aluminum PlateHyeon Jae Shin, Sung-Jin Song
School of Mechanical Engineering and Safety and Structural Integrity Research Center
300 Chunchun-dong, Changan-gu,
Republic of Korea
Lamb wave mode conversions were experimentally studied to utilize the mode conversion characteristics for the nondestructive testing. Aluminum plates with various depths of EDM notches were used for the experiments. The numerical results of Lamb wave dispersion in the plate were given. Short time Fourier transform was employed to obtain the dispersive patterns of the group velocity of the received signals, which represented experimental results of Lamb wave dispersion. Then, the mode identifications were performed by the comparison of the dispersive patterns obtained by numerically and experimentally. For the excitation and reception of the Lamb waves, angle beam transducers with tone burst signals were used. Mode conversion was observed in both pitch-catch and pulse-echo techniques. Mode conversions occurred in forms of phased velocity shift and frequency shift. It showed the possibility of defect detection by using Lamb wave pitch-catch techniques. In addition, by analyzing the characteristics of mode conversion, it may be possible to size defects with Lamb waves.
Keywords: Lamb waves, mode conversion, short time Fourier transform, mode identification, detection, pitch-catch
Lamb waves are known as an efficient means for the nondestructive testing of large area without moving sensors. The capability of Lamb waves to detect and locate defects has been demonstrated in plates and tubing [1-4]. Up to date, the existence of multi modes that are dispersive has been understood and the mode selection concepts were studied for the optimal defect detection [5-7]. Also the mode excitation concepts for the selected mode generation were studied [8-10]. For the identification of dispersive and/or superposed Lamb waves, time-frequency analysis using wavelet transforms  and short time Fourier transforms  were introduced.
In Lamb wave scattering, it is understood that the received modes are distorted from the incident modes. One of the reasons for the distortion is dispersive nature of the impinged Lamb waves. The other reasonable cause of the distortion is the mode conversion that makes energy redistribution among multi modes. It is not only interesting but also valuable to observe the mode conversion to enhance the capability of the Lamb waves in nondestructive testing.
In this study, the mode conversion was observed when Lamb waves were reflected from and transmitted through various sizes of EDM notches in an aluminum plate of 1 mm thick. To identify the Lamb wave modes, the received signals were analyzed in the time-frequency domain that was obtained by short time Fourier transforms. The possibility of the defect detection by using the Lamb wave pitch-catch techniques is discussed. The defect sizing possibility by observing the Lamb wave mode conversion in both the pitch-catch and pulse-echo techniques is also discussed.
An aluminum plate of 1 mm thick was used for the observation of Lamb wave mode conversion. EDM notches of 5%, 20%, 35%, 50%, 65%, and 80% of through wall depth were machined in the aluminum plate. In the pitch-catch transducer set up, the notches were located at the center of the sending and receiving transducers spaced out 30 cm apart. In the pulse-echo experiments, the notches were at 15 cm away from the transducer.
A variable angle beam transducer was used, so that the phase velocity of Lamb waves in both generation and reception could be controlled. The angle was tuned for 20 degrees that corresponded to the phase velocity of 7.9 km/s. Frequency of excited signals was controlled by a tone burst system. In this experiment, four cycles of sine wave was excited at the 5 MHz and the center frequency of the transducers was also 5 MHz.
Phase and group velocity dispersion diagrams of the aluminum plate are shown in Figure 1. The horizontal axis, fd, represents frequency times the thickness of the plate. From the excitation conditions mentioned before, it is possible to indicate the excitation mode in the phase velocity dispersion curves; the mode around A in Fig. 1 (a) may be excited very well in comparison with other modes.
Fig 1: (a) Phase and (b) group velocity dispersion diagrams for Lamb waves in aluminum plate 1 mm thick (+: antisymmetric modes, o: symmetric modes)
Fig. 2 shows the Lamb wave pitch-catch results. For an acquired signal, both time domain signal and time-frequency representation of the signal are given. The time-frequency representations were obtained by short time Fourier transforms. From the time-frequency representation, it was possible to separate the superposed modes and to obtain the patterns of dispersion for each mode, which will make mode identification easy and reliable. Fig. 2 (a) shows the result when Lamb waves were transmitted through flawless area. In this case, the time domain signal looks like superposition of three different wave packets, but the time-frequency analysis of the signal with the measurement of the group velocity reveals that the mode is the predicted mode A. The mode A with frequency bandwidth is indicated in the group velocity dispersion curves as shown in Fig. 1 (b). Fig. 2 (b) shows the pitch-catch result when 5% through wall EDM notch is introduced between the sending and receiving transducers. The result is almost identical with the result for the flawless case as shown in Fig. 2 (a) except over all amplitude changes. However, in the cases that the Lamb wave were transmitted through 35% or 80% through wall EDM notch as shown in Figs. 2 (c) and (d), the time domain signal had a long tail. In fact, the tail is not noise but Lamb waves resulting from superposition of dispersive multi modes that are indicated as C, D, and E. The mode B and a part of mode E are superposed with mode A in time domain signal, because those have similar group velocities. All the modes are identified in dispersion curves as shown in Fig. 1. The phase velocity and fd value of mode B are similar to the incident mode A. For the mode C, the fd value is similar to mode A, but the phase velocity is different. In contrast, the mode D and E have different fd values but the similar phase velocity in comparison with mode A. The results show that the possibility of Lamb wave pitch-catch techniques in defect detection and sizing.
Fig 2: Lamb wave pitch-catch results for (a) no defect, (b) 5%, (c) 35%, and (d) 80% through wall EDM notches in aluminum plate 1 mm thick. The notches were at the center of sending and receiving transducers that were spaced out 30 cm apart.
Fig 3: Lamb wave pulse-echo signals from (a) 5%, (b) 20%, (c) 65% through wall EDM notches and (d) free edge of the aluminum plate 1 mm thick. The notches were at 15 cm away from the transducer.
Lamb waves reflected from and transmitted through various sizes of EDM notches were analyzed in the time-frequency representation obtained by short time Fourier transforms. The mode conversion was observed in forms of both frequency and phase velocity shift. For the same incident Lamb waves, the characteristics of mode conversion were different for the different sizes of notches in both pitch-catch and pulse-echo techniques. It shows the possibility of defect detection by using Lamb wave pitch-catch techniques. In addition, by analyzing the characteristics of Lamb wave mode conversion, it may be possible to size defects for nondestructive testing of plates.
The authors are grateful for the support provided by a grant from the Korea Science & Engineering Foundation (KOSEF) and Safety and Structural Integrity Research Center at the Sungkyunkwan University.
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