Frequency-Dependent Nonreflecting Boundary for Absorbing Lamb Waves Based on Lysmer and Kuhlemeyer Absorbing Boundary
Publication: Journal of Engineering Mechanics
Volume 149, Issue 9
Abstract
This paper reports two nonreflecting boundaries based on the Lysmer and Kuhlemeyer (L-K) absorbing boundary, respectively for absorbing symmetric and antisymmetric Lamb wave, which compensate for the weakness of the L-K absorbing boundary in the application for absorbing Lamb waves at the structural boundary. In this paper, the accurate and approximate formulas of the coefficients of the nonreflecting boundary for symmetric and antisymmetric Lamb waves are obtained by theoretical deduction based on the L-K method. The effectiveness and robustness of these nonreflecting boundaries are verified by comparing with the conventional L-K absorbing boundary in simulation cases. In addition, the limitations of these nonreflective boundaries are discussed.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
This research was funded by the National Natural Science Foundation of China, Grant No. 51975581.
References
Castaings, M., C. Bacon, B. Hosten, and M. V. Predoi. 2004. “Finite element predictions for the dynamic response of thermo-viscoelastic material structures.” J. Acoust. Soc. Am. 115 (3): 1125–1133. https://doi.org/10.1121/1.1639332.
COMSOL Inc. n.d. Structural mechanics module user’s guide version 5.6. Stockholm: COMSOL.
Desiderio, L., S. Fallettab, and L. Scuderib. 2021. “A virtual element method coupled with a boundary integral non reflecting condition for 2D exterior Helmholtz problems.” Comput. Math. Appl. 84 (Feb): 296–313. https://doi.org/10.1016/j.camwa.2021.01.002.
Falcetelli, F., M. B. Romero, S. Pant, E. Troiani, and M. J. Martinez. 2018. “Modelling of pencil-lead break acoustic emission sources using the time reversal technique.” In Proc., 9th European Workshop on Structural Health Monitoring. Manchester, UK: NDT.net.
Giurgiutiu, V. 2014. “Guided waves.” In Structural health monitoring with piezoelectric wafer active sensors, 293–355. New York: Academic Press.
Hosseini, S. M., S. Duczek, and U. Gabbert. 2013. “Non-reflecting boundary condition for Lamb wave propagation problems in honeycomb and CFRP plates using dashpot elements.” Composites, Part B 54 (Nov): 1–10. https://doi.org/10.1016/j.compositesb.2013.04.061.
Jayesh, P., and C. R. Bijudas. 2018. “Online damage detection in metallic cylindrical shells using guided wave modes by time reversal method.” In Advances in structural integrity, 685–694. Singapore: Springer.
Lysmer, J., and R. L. Kuhlemeyer. 1969. “Finite dynamic model for infinite media.” J. Eng. Mech. 95 (4): 859–877. https://doi.org/10.1061/JMCEA3.0001144.
Mulder, W. A. 2021. “A numerically exact nonreflecting boundary condition applied to the acoustic Helmholtz equation.” Geophysics 86 (4): T229–T238. https://doi.org/10.1190/geo2020-0682.1.
Nguyen, K. L., F. Treyssède, and C. Hazard. 2015. “Numerical modeling of three-dimensional open elastic waveguides combining semi-analytical finite element and perfectly matched layer methods.” J. Sound Vib. 344 (May): 158–178. https://doi.org/10.1016/j.jsv.2014.12.032.
Pettit, J. R., A. Walker, P. Cawley, and M. J. Lowe. 2014. “A stiffness reduction method for efficient absorption of waves at boundaries for use in commercial finite element codes.” Ultrasonics 54 (7): 1868–1879. https://doi.org/10.1016/j.ultras.2013.11.013.
Raddatz, F., C. Heinze, C. Dienel, and M. Lingenauber. 2013. “Non-destructive testing and damage assessment of composite aerospace structures using Lamb waves.” In Proc., 4th Int. Workshop on Aircraft System Technologies, 425–436. Hamburg, Germany: DLR.
Rahnema, H., and R. B. Bijari. 2018. “3D numerical modeling of multi-channel analysis of surface wave in homogeneous and layered concrete slabs.” J. Civ. Struct. Health Monit. 8 (1): 161–170. https://doi.org/10.1007/s13349-017-0264-1.
Shen, Y., and C. E. S. Cesnik. 2019. “Nonlinear scattering and mode conversion of Lamb waves at breathing cracks: An efficient numerical approach.” Ultrasonics 94 (Apr): 202–217. https://doi.org/10.1016/j.ultras.2018.09.011.
Shen, Y., and V. Giurgiutiu. 2015. “Effective non-reflective boundary for Lamb waves: Theory, finite element implementation, and applications.” Wave Motion 58 (Nov): 22–41. https://doi.org/10.1016/j.wavemoti.2015.05.009.
Shen, Y., and V. Giurgiutiu. 2016. “Combined analytical FEM approach for efficient simulation of Lamb wave damage detection.” Ultrasonics 69 (Jul): 116–128. https://doi.org/10.1016/j.ultras.2016.03.019.
Skelton, E. A., S. D. Adams, and R. V. Craster. 2007. “Guided elastic waves and perfectly matched layers.” Wave Motion 44 (7–8): 573–592. https://doi.org/10.1016/j.wavemoti.2007.03.001.
Thompson, D. 2008. “A continuous damped vibration absorber to reduce broad-band wave propagation in beams.” J. Sound Vib. 311 (3–5): 824–842. https://doi.org/10.1016/j.jsv.2007.09.038.
Wang, Z., P. Qiao, and B. Shi. 2018. “Effective time-frequency characterization of Lamb wave dispersion in plate-like structures with non reflecting boundaries.” Smart Struct. Syst. 21 (2): 195–205. https://doi.org/10.12989/sss.2018.21.2.195.
Yu, Z., C. Xu, J. Sun, and F. Du. 2021. “Guided wave propagation analysis in stiffened panel using time-domain spectral finite element method.” Chin. J. Aeronaut. 35 (10): 208–221. https://doi.org/10.1016/j.cja.2021.11.014.
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© 2023 American Society of Civil Engineers.
History
Received: Dec 11, 2022
Accepted: Mar 31, 2023
Published online: Jun 19, 2023
Published in print: Sep 1, 2023
Discussion open until: Nov 19, 2023
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