Journal of Mechanical Science and Technology

, Volume 33, Issue 1, pp 87–94 | Cite as

Analysis of edge defects in an elastic plate using SH-waves

  • Brahim Mohammedi
  • Nahil A. SobhEmail author
  • Diab Abueidda
  • Belgacem-Bouzida Aissa


The interaction of guided SH-waves with the beveled free end of a semi-infinite plate is analytically and numerically investigated. The material of the plate is assumed to be elastic, homogenous, and isotropic. The plate is modeled as a combination of a semi-infinite region and bounded wedged region separated by a common boundary. The analytical solution of the vertical free end case for the two regions is derived and used in verifying the numerical implementation. In this study, the SH0 and the SH1 first two incident modes are individually applied to analyze the corresponding reflected modes from the free end. Specifically, the elastic energy carried by the reflected modes is reported for a wide range of beveled angles and incident frequencies.


Bevel end Edge defects Elastic plate SH waves Wave function 


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  1. [1]
    J. B. Lawrie and J. Kaplunov, Edge waves and resonance on elastic structures: an overview, Mathematics and Mechanics of Solids, 17 (2012) 4–16.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    E. Deckers, O. Atak, L. Coox, R. D’Amico, H. Devriendt, S. Jonckheere, K. Koo, B. Pluymers, D. Vandepitte and W. Desmet, The wave based method: An overview of 15 years of research, Wave Motion, 51 (2014) 550–565.MathSciNetCrossRefGoogle Scholar
  3. [3]
    V. Giurgiutiu, Structural health monitoring: with piezoelectric wafer active sensors, Academic Press, MA, USA (2007).Google Scholar
  4. [4]
    W. Ostachowicz, P. Kudela, M. Krawczuk and A. Zak, Guided waves in structures for SHM: The time-domain spectral element method, John Wiley & Sons, West Sussex, UK (2011).zbMATHGoogle Scholar
  5. [5]
    J. L. Rose, Ultrasonic guided waves in solid media, Cambridge University Press, NY, USA (2014).CrossRefGoogle Scholar
  6. [6]
    J. L. Rose, Guided wave nuances for ultrasonic nondestructive evaluation, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 47 (2000) 575–583.CrossRefGoogle Scholar
  7. [7]
    H. Gao, S. Ali and B. Lopez, Efficient detection of delamination in multilayered structures using ultrasonic guided wave EMATs, NDT & E International, 43 (2010) 316–322.CrossRefGoogle Scholar
  8. [8]
    M. Hirao and H. Ogi, An SH-wave EMAT technique for gas pipeline inspection, NDT & E International, 32 (1999) 127–132.Google Scholar
  9. [9]
    Z. Abduljabbar, S. Datta and A. Shah, Diffraction of horizontally polarized shear waves by normal edge cracks in a plate, Journal of Applied Physics, 54 (1983) 461–472.CrossRefGoogle Scholar
  10. [10]
    J.-J. Chen, G.-H. Song and X. Han, Asymmetric first order shear horizontal guided waves propagation in a tapered plate, Physics Letters A, 379 (2015) 2125–2129.CrossRefGoogle Scholar
  11. [11]
    J. J. Ditri, Some results on the scattering of guided elastic SH waves from material and geometric waveguide discontinuities, The Journal of the Acoustical Society of America, 100 (1996) 3078–3087.CrossRefGoogle Scholar
  12. [12]
    N. Nakamura, H. Ogi, M. Hirao and K. Nakahata, Mode conversion behavior of SH guided wave in a tapered plate, NDT & E International, 45 (2012) 156–161.Google Scholar
  13. [13]
    Z. Ahmad and U. Gabbert, Simulation of Lamb wave reflections at plate edges using the semi-analytical finite element method, Ultrasonics, 52 (2012) 815–820.CrossRefGoogle Scholar
  14. [14]
    N. Wilkie-Chancellier, H. Duflo, A. Tinel and J. Duclos, Theoretical study of lamb wave conversion at the edge of different angles bevelled plates, Forum Acusticum, Seville (2002) 17–21.Google Scholar
  15. [15]
    M. Mofakhami and C. Boller, Lamb wave interactions with non-symmetric features at structural boundaries, Zeitschrift für Angewandte Mathematik und Mechnik (ZAMM) (2008).CrossRefzbMATHGoogle Scholar
  16. [16]
    N. Wilkie-Chancellier, H. Duflo, A. Tinel and J. Duclos, Numerical description of the edge mode at the beveled extremity of a plate, The Journal of the Acoustical Society of America, 117 (2005) 194–199.CrossRefGoogle Scholar
  17. [17]
    M. Castaings, E. Le Clezio and B. Hosten, Modal decomposition method for modeling the interaction of Lamb waves with cracks, The Journal of the Acoustical Society of America, 112 (2002) 2567–2582.CrossRefGoogle Scholar
  18. [18]
    B. Morvan, N. Wilkie-Chancellier, H. Duflo, A. Tinel and J. Duclos, Lamb wave reflection at the free edge of a plate, Journal of the Acoustical Society of America, 113 (2003) 1417–1425.CrossRefGoogle Scholar
  19. [19]
    N. Wilkie-Chancellier, H. Duflo, A. Tinel and J. Duclos, Energy balance in the conversion of a Lamb wave at a bevelled edge, Acta Acustica United with Acustica, 90 (2004) 77–84.Google Scholar
  20. [20]
    S. Santhanam and R. Demirli, Reflection of Lamb waves obliquely incident on the free edge of a plate, Ultrasonics, 53 (2013) 271–282.CrossRefGoogle Scholar

Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Brahim Mohammedi
    • 1
    • 2
  • Nahil A. Sobh
    • 2
    Email author
  • Diab Abueidda
    • 3
  • Belgacem-Bouzida Aissa
    • 4
  1. 1.Laboratoire de Recherche en ProductiqueUniversity Mostefa Benboulaid Batna2BatnaAlgeria
  2. 2.Beckman Institute for Advanced Science and TechnologyUniversity of Illinois at Urbana-ChampaignChampaignUSA
  3. 3.Department of Mechanical Science and EngineeringUniversity of Illinois at Urbana-ChampaignChampaignUSA
  4. 4.Department of PhysicsUniversity of Batna1BatnaAlgeria

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