Electronic Journal Technical Acoustics ISSN 1819-2408

M. El Allami, H. Rhimini, A. Nassim, M. Sidki

Application of the wavelet transform analysis to Lamb modes signals in plates

language: English

received 25.01.2010, published 29.04.2010

Download article (PDF, 215 kb, ZIP), use browser command "Save Target As..."
To read this document you need Adobe Acrobat © Reader software, which is simple to use and available at no cost. Use version 4.0 or higher. You can download software from Adobe site (http://www.adobe.com/).

ABSTRACT

The paper proposes a wavelet spectral analysis method of Lamb waves in thin isotropic plates. A numerical code is developed on the Comsol Multiphysics software to solve, by the finite element method, the equation of motion and determine the displacement field. The post processing of the obtained displacement field is done, on the Matlab software, by a method based on the wavelet transform (WT). The considered application aims to determine the dispersion curves of symmetric S0 and anti symmetric A0 Lamb modes of a plane steel plate. These curves are obtained by the WT of displacement field and are compared to the analytic curves. Several mother wavelets are tested showing that the complex mother wavelet Shan 1-1.5 gives the better agreement.

Keywords: lamb wave, ultrasound, finite element method, wavelets.

10 pages, 8 figures

Сitation: M. El Allami, H. Rhimini, A. Nassim, M. Sidki. Application of the wavelet transform analysis to Lamb modes signals in plates. Electronic Journal “Technical Acoustics”, http://www.ejta.org, 2010, 8.

REFERENCES

1. D. Alleyne, P. Cawley. A two-dimensional Fourier transform method for the measurement of propagating multimode signals. J. Acoust. Soc. Am, 1991, 89(3), 1159–1168.
2. F. Moser. Modeling elastic wave propagation in waveguides with the finite element method. NDT&E International, 1999, 32, 225–234.
3. I. Daubechies. The wavelet transform, time–frequency localization and signal analysis. IEEE Transactions on Information Theory, 1990, 36 (5), 961–1005.
4. D. E. Newland. Wavelet analysis of vibration, part I: theory. Journal of Vibration and Acoustics, 1994, 116, 409–416.
5. Y. Hayashi et al. Non-contact estimation of thickness and elastic properties of metallic foils by the wavelet transform of laser-generated Lamb waves. NDT&E Int, 1999, 32, 21–27.
6. Hyunjo Jeong, Young-Su Jang. Wavelet analysis of plate wave propagation in composite laminates. Composite Structures, 2000, 49, 443–450.
7. Y. Y. Kim, E. H. Kim. Effectiveness of the continuous wavelet transform in the analysis of some dispersive elastic waves. Journal of the Acoustical Society of America, 2001, 110, 1–9.
8. M. Lemistre, D. L. Balageas, Structural health monitoring system based on diffracted Lamb wave analysis by multiresolution processing. Smart Materials and Structures, 2001, 10, 504–511.
9. S. S. Kessler, S. M. Spearing, C. Soutis. Damage detection in composite materials using Lamb wave methods. Smart Materials and Structures, 2002, 11, 269–278.
10. C. A. Paget, S. Grondel, K. Levin, C. Delebarre. Damage assessment in composites by Lamb waves and wavelet coefficients. Smart Materials and Structures, 2003, 12, 393–402.
11. P. Rizzo, I. Bartoli, A. Marzani, F. L. Scalea. Defect classification in pipes by neural networks using multiple guided ultrasonic wave features extracted after wavelet processing. Journal of Pressure Vessel Technology, 2005, 3, 294–303.
12. F. Jenot, M. Ouaftouh, W.-J. Xu, M. Duquennoy, M. Ourak. Inclusions detection using Lamb waves in flexible printed circuits. Ultrasonics, 2006, 44, e1163–e1167.
13. J. Grabowska, M.Palacz, M. Krawczuk. Damage identification by wavelet analysis. Mechanical Systems and Signal Processing, 2008, 2008.01.003, 1–13.
14. H. Lamb. On waves in an elastic plate. Poc.Roc.Soc London, Ser. A. 1917.
15. I. A. Viktorov. Rayleigh and Lamb waves. Plenum Press New York, 1970.
16. S. Basseville, F Feyel. Méthodes de résolution en éléments finis. Ecole Nationale Supérieure des Mines de Paris, Enseignement spécialisé «Eléments finis» S3733–S3735, http://mms2.ensmp.fr/ef_paris/technologie/polycop/f_coursMR.pdf
17. G. Dhatt, G. Touzot. Une représentation de la méthode des éléments finis. Maloine SA. Editeur Paris, 1984, Deuxième edition.
18. S. Mallat. A Wavelet tour of signal processing. Academic press, New York, 1999.
19. I. Daubechies. Ten lecture on Wavelets. SIAM Publications, 1992.
20. C. K. Chui. An introduction to wavelets. San Diego, CA: Academic Press, 1992.
21. K. Kishimoto, H. Inoue, M. Hamada, T. Shibuya. Time frequency analysis of dispersive waves by means of wavelet transforms. J Appl Mech, 1995, 62, 841–846.

		Mhammed EL ALLAMI received master degree from Faculty of sciences, EL Jadida, Morocco. He has published 2 publications and communications on the finite element modelling of Lamb modes signals in plates. Presently he is a PhD student at Chouaib Doukkali University, El Jadida, Morocco. E-mail: m.elallami(at)hotmail.com
		Hassan RHIMINI received his master and PhD from Chouaib Doukkali University, EL Jadida, Morocco. He has published over 12 publications and communications on modelling of Lamb modes signals in plates. Hassan Rhimini is a PhD student at Chouaib Doukkali University, El Jadida, Morocco. E-mail: hrhimini(at)yahoo.fr
		Abdelkarim NASSIM received his master from University of Pau, Pau, France and PhD from Chouaib Doukkali University, El Jadida, Morocco. He has published over 36 publications and communications on optics and wavelets. Abdelkarim Nassim is a Research Professor at Chouaib Doukkali University, El Jadida, Morocco. E-mail: knassim58(at)yahoo.fr
		Mouncif SIDKI received his master from Paul Sabatier University, Toulouse, France and PhD from Sherbrooke University, Sherbrooke, Canada. He has published over 35 publications and communications on acoustics and modelling of ultrasound propagation. Mouncif Sidki is a Research Professor at Chouaib Doukkali University, El Jadida, Morocco E-mail: sidkimouncif(at)hotmail.com