Engineering Transactions, 72, 2, pp. 203–224, 2024

Wavelet Analysis of Ultrasonic Lamb Wave Displacements in Three-Layer Adhesive Plates: Continuous Wavelet Transform (CWT) versus the Semi-Analytical Finite Element Method (SAFEM)

Abdelali YACOUBI
Hassan I University

ORCID ID 0000-0002-8624-2339
Hassan I University

Mustapha AZKOUR
ORCID ID 0009-0009-2545-7043
Hassan II University

ORCID ID 0009-0006-1149-8811
Hassan I University

ORCID ID 0009-0009-5774-9331
1) Hassan I University 2) Regional Center for Education and Training Professions (CRMEF)

In this paper, we aim to identify the most appropriate mother wavelet for analyzing the displacements of ultrasonic guided waves in tri-layered adhesive plates.We determine the group velocities of a given mode using various mother wavelets. The precision of each mother wavelet is evaluated by comparing the values of the group velocities with those found by the semianalytical finite element method (SAFEM). The most appropriate mother wavelet function can then be used to study tri-layered adhesive plates with defects.
Keywords: Shannon wavelet; ultrasonic guided waves; bonded structures; signal processing; FEM
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Zhang X., Yuan S., Hao T., Lamb wave propagation modeling for structure health monitoring, Frontiers of Mechanical Engineering in China, 4(3): 326–331, 2009, doi: 10.1007/s11465-009-0045-6.

Malinowski P.H., Ecault R., Wandowski T., Ostachowicz W.M., Evaluation of adhesively bonded composites by nondestructive techniques, [in:] in Proceedings Volume 10170, Health Monitoring of Structural and Biological Systems 2017; SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, 2017, doi: 10.1117/12.2259852.

Daubechies I., The wavelet transform, time-frequency localization and signal analysis, IEEE Transactions on Information Theory, 36(5): 961–1005,1990, doi: 10.1109/18.57199.

Newland D.E., Wavelet analysis of vibration: Part 1 – Theory, Journal of Vibration and Acoustics, 116(4): 409–416, 1994, doi: 10.1115/1.2930443.

Hayashi Y., Ogawa S., Cho H., Takemoto M., Non-contact estimation of thickness and elastic properties of metallic foils by laser-generated Lamb waves, NDT & E International, 32(1): 21–27, 1999, doi: 10.1016/S0963-8695(98)00029-2.

Jeong H., Jang Y.-S., Wavelet analysis of plate wave propagation in composite laminates, Composite Structures, 49(4): 443–450, 2000, doi: 10.1016/S0263-8223(00)00079-9.

El Allami M., Rhimini H., Nassim A., Sidki M., Application of the wavelet transform analysis to Lamb modes signals in plates, Electronic Journal Technical Acoustics,, 2010, 8.

El Allami M., Rhimini H., Sidki M., Application of the complex mother wavelet Shan 1-1.5 processing to lamb modes signals in plates, International Journal of Science and Research (IJSR), 4 (1): 1849–1854, 2015.

Paget C.A., Grondel S., Levin K., Delebarre C., Damage assessment in composites by Lamb waves and wavelet coefficients, Smart Materials and Structures, 12(3): 393, 2003, doi: 10.1088/0964-1726/12/3/310.

Zima B., Rucka M., Application of wavelet transform in analysis of guided wave propagation signals for damage detection in a steel plate, Diagnostyka, 16(2): 43–48, 2015.

Douka E., Loutridis S., Trochidis A., Crack identification in plates using wavelet analysis, Journal of Sound and Vibration, 270(1-2): 279–295, 2004, doi: 10.1016/S0022-460X(03)00536-4.

Li F., Meng G., Kageyama K., Su Z., Ye L., Optimal mother wavelet selection for Lamb wave analyses, Journal of Intelligent Material Systems and Structures, 20(10): 1147–1161, 2009, doi: 10.1177/1045389X09102562.

Zhao G., Wang B., Wang T., Hao W., Luo Y., Detection and monitoring of delamination in composite laminates using ultrasonic guided wave, Composite Structures, 225: 11161, 2019, doi: 10.1016/j.compstruct.2019.111161.

Sha G., Radzienski M., Soman R., Wandowski T., Cao M., Ostachowicz W., Delamination imaging in laminated composite plates using 2D wavelet analysis of guided wavefields, Smart Materials and Structures, 30(1): 015001, 2021, doi: 10.1088/1361-665X/abc66b.

Hameed M.S., Li Z., Zheng K., Damage detection method based on continuous wavelet transformation of Lamb wave signals, Applied Sciences, 10(23): 8610, 2020; doi: 10.3390/app10238610.

Feng B., Ribeiro A.L., Ramos H.G., A new method to detect delamination in composites using chirp-excited Lamb wave and wavelet analysis, NDT & E International, 100: 64–73, 2018, doi: 10.1016/j.ndteint.2018.08.004.

Liu B., Liu T., Meng F., Research on Morlet wavelet based Lamb wave spatial sampling signal optimization method, Journal of Shanghai Jiaotong University, 23(Suppl 1): 61–69, 2018, doi: 10.1007/s12204-018-2024-8.

Viola E., Marzani A., Bartoli I., Semi-analytical formulation for guided wave propagation, [in] Elishakoff I. (Ed.), Mechanical Vibration: Where do we Stand?, International Centre for Mechanical Sciences, vol 488, pp. 105–121, Springer, Vienna, 2007, doi: 10.1007/978-3-211-70963-4_6.

Rose J. L., Ultrasonic Guided Waves in Solid Media, Cambridge University Press, New York, 2014.

Zitouni I., Rhimini H., Chouaf. A, Comparative study of the spectral method, DISPERSE and other classical methods for plotting the dispersion curves in anisotropic plates, Journal of Applied and Computational Mechanics, 9(4): 955–973, 2023, doi: 10.22055/jacm.2023.42530.3941.

Galán J.M., Abascal R., Numerical simulation of Lamb wave scattering in semi-finite plates, International Journal for Numerical Methods in Engineering, 53(5): 1145–1173, 2001, doi: 10.1002/nme.331.

Lamb H., On the vibrations of an elastic sphere, Proceedings of the London Mathematical Society. s1-13(1): 189–212, 1881, doi: 10.1112/plms/s1-13.1.189.

Vázquez S., Gosálbez J., Bosch I., CarriónA., Gallardo, C., Payá J., Comparative study of coupling techniques in Lamb wave testing of metallic and cementitious plates, Sensors, 19(19): 4068, 2019, doi: 10.3390/s19194068.

Graps A., An introduction to wavelets, IEEE Computational Science & Engineering, 2 (2): 50–61, 1995, doi: 10.1109/99.388960.

Ng C.T., Veidt M., Rose L.R.F., Wang C.H., Analytical and finite element prediction of Lamb wave scattering at delaminations in quasi-isotropic composite laminates, Journal of Sound and Vibration, 331(22): 4870–4883, 2012, doi: 10.1016/j.jsv.2012.06.002.

Veidt M., Ng C.T., Influence of stacking sequence on scattering characteristics of the fundamental anti-symmetric Lamb wave at through holes in composite laminates, The Journal of the Acoustical Society of America, 129(3): 1280–1287, 2011, doi: 10.1121/1.3533742.

DOI: 10.24423/EngTrans.3207.2024