Skip to main content
SpringerLink
Log in

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

  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  3. V. Giurgiutiu, Structural health monitoring: with piezoelectric wafer active sensors, Academic Press, MA, USA (2007).

    Google Scholar 

  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).

    MATH  Google Scholar 

  5. J. L. Rose, Ultrasonic guided waves in solid media, Cambridge University Press, NY, USA (2014).

    Book  Google Scholar 

  6. J. L. Rose, Guided wave nuances for ultrasonic nondestructive evaluation, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 47 (2000) 575–583.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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. 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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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. 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.

    Article  Google Scholar 

  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. M. Mofakhami and C. Boller, Lamb wave interactions with non-symmetric features at structural boundaries, Zeitschrift für Angewandte Mathematik und Mechnik (ZAMM) (2008).

    Book  MATH  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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. S. Santhanam and R. Demirli, Reflection of Lamb waves obliquely incident on the free edge of a plate, Ultrasonics, 53 (2013) 271–282.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Recherche en Productique, University Mostefa Benboulaid Batna2, Batna, Algeria

    Brahim Mohammedi

  2. Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Champaign, USA

    Brahim Mohammedi & Nahil A. Sobh

  3. Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Champaign, USA

    Diab Abueidda

  4. Department of Physics, University of Batna1, Batna, Algeria

    Belgacem-Bouzida Aissa

Authors
  1. Brahim Mohammedi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nahil A. Sobh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Diab Abueidda
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Belgacem-Bouzida Aissa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nahil A. Sobh.

Additional information

Recommended by Associate Editor Junhong Park

Brahim Mohammedi received his M.S. in mechanical engineering from the University of Colorado at Boulder USA. He is currently a lecturer at the Faculty of Technology, University of Batna 2. His research interests include solid mechanics, waves in elastic solids and elasticity problems.

Diab Abueidda received his M.Sc. in mechanical engineering from Masdar Institute of Science and Technology and his B.Sc. from American University of Sharjah. Both are in the United Arab Emirates. Currently, he is a Ph.D. student at the University of Illinois at Urbana-Champaign. His research interest includes computational and experimental solid mechanics, topology optimization, and nano-/micro-fabrication.

Nahil A. Sobh received his Ph.D. in Applied Mathematics and Ph.D. in Civil engineering from the University of Colorado at Boulder USA. He is currently lead scientist of Beckman Institute for Advanced Science and Technology, Carl R. Woese Institute for Genomic Biology, Department of Civil and Environmental Engineering, and an Adjunct Associate Professor at Department of Mechanical Science and Technology. He currently leads the Data Science Implementation project of the NIH center of Excellence on the Big Data to Knowledge. His research interests include big data, data science, artificial intelligence, deep learning, and computational and experimental mechanics.

Belgacem-Bouzida Aissa received his Doctorat en Sciences in Material engineering from the University of Nancy I France. He is currently a Professor at the Department of Physics and Vice-President of the University of Batna 1, Algeria. He has published more than 40 papers in different journals and conferences. His research interests are materials and phase diagrams of multicomponents. alloys. He is a supervisor of many scientific research projects.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mohammedi, B., Sobh, N.A., Abueidda, D. et al. Analysis of edge defects in an elastic plate using SH-waves. J Mech Sci Technol 33, 87–94 (2019). https://doi.org/10.1007/s12206-018-1209-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-018-1209-2

Keywords

Search

Navigation