Damage localization in metallic plates through lamb wave frequency variation: A numerical study

Damage localization in metallic plates through lamb wave frequency variation: A numerical study

Deepak Kumar, Sahil Kalra

Abstract. Lamb wave is extensively used in the structural health monitoring (SHM) of various structures for defect detection. However, the Lamb wave is constrained by two interlinked complexities: inherent dispersion and multimode characteristics. The presence of many dispersive modes poses challenges in their application for structural damage localization. The aim of this work is to examine Lamb wave behavior and determine the location of the damage when its central frequency varies in the range specified by its dispersion curve for a particular structural thickness. The analysis methodology is illustrated by twenty numerically simulated cases of aluminium plates using a three-dimensional finite element method (FEM) in Abaqus/CAE. A hole as a defect is included in the plate that extends through its entire thickness. The fundamental symmetric Lamb mode (S0) with increasing central frequency in the chosen range is actuated in the first ten cases as it exhibits minimal dispersion. History output for the out-of-plane components of the signal is obtained, which is used for damage location imaging using Matlab. A similar approach is repeated for the next ten cases using the fundamental anti-symmetric mode (A0). The images obtained for the damage locations show a clear distinction among the accuracy of Lamb wave frequencies that are used. As the central frequency is increased for S0 mode, the size of the located damage area increases, resulting in a decrease in the optimization of damage localization. Whereas a reverse output is observed with the A0 mode, where the localized area decreases with increases in frequency. In all cases, the location is accurately localized. However, the estimated area of damage is shifted from its central location. Another significant outcome from this investigation showed that at a higher frequency range, the localized area of the damage is approximately the same. The investigation concludes that low-frequency Lamb modes are better suited for damage localization using imaging techniques. It is also confirmed by the investigation that the low-frequency Lamb wave gives better localization results when applied to identifying comparatively large defects (in mm).

Keywords
Lamb Wave, FEM, SHM, Damage Imaging, Dispersion Curve

Published online 3/25/2025, 7 pages
Copyright © 2025 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: Deepak Kumar, Sahil Kalra, Damage localization in metallic plates through lamb wave frequency variation: A numerical study, Materials Research Proceedings, Vol. 50, pp 98-104, 2025

DOI: https://doi.org/10.21741/9781644903513-11

The article was published as article 11 of the book Structural Health Monitoring

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

References
[1] H. Lamb, Proc. Roy. Soc. (London) A90, 111, 114 (1916).
[2] D. C. Worlton; Experimental Confirmation of Lamb Waves at Megacycle Frequencies. J. Appl. Phys. 1 June 1961; 32 (6): 967–971.
[3] Kumar, Deepak, Sahil Kalra, and Mayank Shekhar Jha. “Recent advancements on structural health monitoring using lamb waves.” Computational and Experimental Methods in Mechanical Engineering: Proceedings of ICCEMME 2021. Springer Singapore, 2022. https://doi.org/10.1007/978-981-16-2857-3_15
[4] Zhang, G., Kundu, T., Deymier, P. A., & Runge, K. (2024). Defect localization in plate structures using the geometric phase of Lamb waves. Ultrasonics, 107492. https://doi.org/10.1016/j.ultras.2024.107492
[5] Zheng, S., Luo, Y., Xu, C., & Xu, G. (2023). A review of laser ultrasonic lamb wave damage detection methods for thin-walled structures. Sensors, 23(6), 3183. https://doi.org/10.3390/s23063183
[6] Ling, F., Chen, H., Lang, Y., Yang, Z., Xu, K., & Ta, D. (2023). Lamb wave tomography for defect localization using wideband dispersion reversal method. Measurement, 216, 112965. https://doi.org/10.1016/j.measurement.2023.112965
[7] Huang, L., Luo, Z., Zeng, L., & Lin, J. (2024). Detection and localization of corrosion using the combination information of multiple Lamb wave modes. Ultrasonics, 138, 107246. https://doi.org/10.1016/j.ultras.2024.107246
[8] Giurgiutiu, Victor. “Tuned Lamb wave excitation and detection with piezoelectric wafer active sensors for structural health monitoring.” Journal of intelligent material systems and structures 16.4 (2005): 291-305. https://doi.org/10.1177/1045389X05050106
[9] Rabbi, M. S., Teramoto, K., Ishibashi, H., & Roshid, M. M. (2023). Imaging of sub-surface defect in CFRP laminate using A0-mode Lamb wave: Analytical, numerical and experimental studies. Ultrasonics, 127, 106849. https://doi.org/10.1016/j.ultras.2022.106849
[10] Zhang, N., Zhai, M., Zeng, L., Huang, L., & Lin, J. (2023). Damage assessment using the Lamb wave factorization method. Mechanical Systems and Signal Processing, 190, 110128. https://doi.org/10.1016/j.ymssp.2023.110128
[11] Xu, H., Liu, L., Xu, J., Xiang, Y., & Xuan, F. Z. (2024). Deep learning enables nonlinear Lamb waves for precise location of fatigue crack. Structural Health Monitoring, 23(1), 77-93. https://doi.org/10.1177/14759217231167076
[12] Ruzzene, Massimo. “Frequency–wavenumber domain filtering for improved damage visualization.” Smart materials and structures 16.6 (2007): 2116. https://doi.org/10.1088/0964-1726/16/6/014
[13] Michaels, Thomas E., Jennifer E. Michaels, and Massimo Ruzzene. “Frequency–wavenumber domain analysis of guided wavefields.” Ultrasonics 51.4 (2011): 452-466. https://doi.org/10.1016/j.ultras.2010.11.011
[14] SIMULIA, Abaqus/CAE 2021, Version 6.22. Dassault Syst`emes Simulia Corp, Johnston, RI, United States.
[15] MathWorks, MATLAB (R2022b). The MathWorks Inc., Natick, Massachusetts, United States.