Tone-Burst Generations of Circumferential Guided Waves Propagating in a Pipe and Their Time-Frequency Analyses

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Hideo Nishino, Ryuji Yokoyama and Kenichi Yoshida (The Univ. of Tokushima)

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1. Introduction Guided waves propagating in the axial direction of pipe [1] have been anticipated for an efficient nondestructive inspection tecnique because of their capability of long range propagation. On the other hand, in the guided wave propagating in axial direction, sensitivity for a small defect is very poor because the used frequency is very low (20-100 kHz). Recently, guided waves propagating in the circumferential direction of a pipe (Circumferential guided waves: CGWs) [2,3] have been in the spotlight as one of the improved method for a small defect detection. While an inspection area of the CGW is restricted in the circumferential area, the sensitivity for a small defect is high due to the high frequency (0.5-5 MHz) used. The authors have already reported [4,5] a simple generation method of the CGWs (C-SH and C-Lamb waves) using a single bulk shear wave sensor (SWS). In the previous method, the selective generation of the C-SH and C-Lamb waves was realized by changing the polarization direction of the SWS is parallel or vertical to the axial direction of the pipe. In this paper, wide range selective generation of the CGW are proposed by using tone-burst signals with several center-frequencies. Generated CGWs are verified with time-frequency analyses in comparison to the theoretical dispersion relations. 2. Wide range generation and analysis

A wide range generation and analysis of the CGW could be achieved using a number of tone-burst sources determined by required frequency range and step. The wavelet transformation is recursively applied to each received signal to calculate a wavelet coefficient at each frequency step as a function of propagation time. All of the wavelet coefficients (having different center frequencies) are combined to form a

gray-scale representation as a wide range time-frequency analysis result. Experiments were carried out with a SWS having a 3.7 MHz center frequency. An aluminum pipe having 30 mm outer diameter and 1 mm wall-thickness was used in the experiments (Fig. 1). nishino@me.tokushima-u.ac.jp

Fig. 1 Experimental setup.

Fig. 2 Result of the present analysis for the C-SH wave generated by 1 cycle rectangular pulse

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Fig. 3 Result of the present analysis for the C-SH wave generated by 10 cycles rectangular pulse

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Proceedings of Symposium on Ultrasonic Electronics, Vol.28, (2007), pp. 191-19214-16 November, 20072-02-02

3. Results Figure 2 shows a time-frequency result of the C-SH waves generated by one cycle tone burst. A time-frequency result of the C-SH wave having ten cycles tone bursts is also shown in Fig. 3. Lines in Figs. 2 and 3 are the theoretical dispersion relations [5] of the propagation modes as functions of time and frequency. The result in Fig. 2 was agreed with the theoretical dispersion relations only at around the center frequency of the SWS. In contrast to this, the experimental result in Fig. 3 was agreed very well with the theory in the wide frequency range except the frequency lower than 2.5 MHz. In comparison to the one cycle case, the 10 cycles tone burst has relatively wide ranginess and high frequency resolution. Figure 4 shows the normalized time-frequency result of Fig. 3. The normalized result was obtained to divide wavelet coefficients by the maximum values of themselves at every frequency steps to emphasize the weak amplitudes due to the frequency characteristics of the SWS. Because of the emphasis by the normalization in Fig. 4, we can easily confirm the propagation modes in weak amplitude region ranging from 1 MHz to 2.5 MHz. A time-frequency result of the C-Lamb wave having 10 cycles tone burst and its normalized result are shown in Figs. 5 and 6, respectively. The obtained results were in good agreement with the theoretical dispersions especially in the modes having high velocities (near the longitudinal wave velocity, 20-30µs propagation time). Because the tangential vibration of a SWS is the generation source of the C-Lamb waves, the modes having a large tangential particle displacement can be efficiently generated [5]. 4. Conclusion To obtain wide range generation and analysis of the circumferential guided wave (CGW), we have proposed the simple generation method with a bulk shear wave sensor as well as several tone-burst signals and the wavelet transformation. In the experimental verifications using a 30 mm outer diameter and 1 mm thick Al pipe, the obtained dispersion relations using 10 cycles tone-burst signals were agreed well with the theory. Normalized wavelet coefficient is also effective to identify the propagation modes of weak signals due to low sensitivity frequency region of a sensor. Reference 1. H. Nishino et al: JJAP 40 (2001) 354 2. M. Hirao et al: NDT&E, 32 (1999) 127 3. H. Nagamizo et al: Proc. ASME PVP (2003) 7 4. H. Nishino et al: Acoust. Sci. Tech. 27 (2006)389 5. H. Nishino et al: JJAP 46 (2007) 4568 6. T. Hayashi: Personal communication

Fig. 4 Normalized result of the C-SH wave generated by 10 cycles rectangular pulse

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Fig. 5 Result of the C-Lamb wave generated by 10 cycles rectangular pulse

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Fig. 6 Normalized result of the C-Lamb wave generated by 10 cycles rectangular pulse

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