Skip to main content
SpringerLink
Log in

Numerical simulation of wave propagation using spectral finite elements

  • Original Paper
  • Published:
CEAS Aeronautical Journal Aims and scope Submit manuscript

Abstract

For the analysis of wave propagation at high frequencies, the spectral finite element method is under investigation. In contrast to the conventional finite element method, high-order shape functions are used. They are composed of Lagrange polynomials with nodes at the Gauss–Lobatto–Legendre points. The Gauss–Lobatto–Legendre integration scheme is applied in order to obtain a diagonal mass matrix. The resulting system equations can be solved efficiently. In the numerical examples, spectral finite elements with shape functions of different order are applied to a plane strain problem. The numerical examples cover structures without and with stiffness discontinuities. It is shown that the results agree well with analytical and experimental solutions.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Achenbach, J.D.: Wave propagation in elastic solids. North-Holland, Amsterdam (1973)

  2. Auricchio, F., Taylor, R.L.: A shear deformable plate element with an exact thin limit. Comp. Meth. Appl. Mech. Eng. 118, 393–412 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  3. Durufle, M., Grob, P., Joly, P.: Influence of Gauss and Gauss–Lobatto quadrature rules on the accuracy of a quadrilateral finite element method in the time domain. Numer. Methods Partial Differ. Equ. 25, 526–551 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ende S.v.: Transient angeregte lamb-wellen in elastischen und viskoelastischen platten. Ph.D. thesis, Helmut-Schmidt-Universität, Hamburg (2008)

  5. Ende, S.v., Lammering, R.: Investigation on piezoelectrically induced Lamb wave generation and propagation. Smart Mater. Struct. 16, 1802–1809 (2007)

    Article  Google Scholar 

  6. Giurgiutiu, V.: Structural Health Monitoring—With Piezoelectric Wafer Active Sensors. Academic Press, Amsterdam (2008)

  7. Graff, K.F.: Wave Motion in Elastic Solids. Clarendon Press, Oxford (1975)

  8. Hughes, T.J.R.: The Finite Element Method. Dover Publications, New York (2000)

  9. Komatitsch, D., Tromp, J.: Introduction to the spectral element method for three-dimensional seismic wave propagation. Geophys. J. Int. 139, 806–822 (1999)

    Article  Google Scholar 

  10. Lammering, R., Eremin, A., Neumann, M., Gabbert, U., Hosseini, S.M.H.: Structural health monitoring of lightweight structures by use of lamb waves. In: Proceedings 2nd International Symposium on NDT in Aerospace 2010 (2010). http://www.ndt-aerospace.com/Portals/aerospace2010/BB/we1b3.pdf

  11. Lammering, R., Neumann, M.: Optical measurement techniques for use of defect detection in thin walled structures. In: Proceedings of the 5th European Workshop on Structural Health Monitoring, Sorrento, Italy, Vol. 1, pp. 517–522 (2010)

  12. Mackerle, J.: Finite-element modelling of non-destructive material evaluation, an addendum: a bibliography. Model. Simul. Mater. Sci. Eng. 12, 709–834 (1997−2003)

    Google Scholar 

  13. Mindlin, R.D.: Influence of rotatory inertia and shear in flexural motion of isotropic elastic plates. J. Appl. Mech. 18, 31–38 (1951)

    MATH  Google Scholar 

  14. Reissner, E.: The effect of transverse shear deformation on the bending of elastic plates. J. Appl. Mech. 12, 69–76 (1945)

    MathSciNet  Google Scholar 

  15. Schade, H., Neemann, K.: Tensoranalysis. de Gruyter (2006)

  16. Schulte, R.T., Fritzen, C.P.: Simulation of wave propagation in damped composite structures with piezoelectric coupling. J. Theor. Appl. Mech. 49(3), 879–903 (2011)

    Google Scholar 

Download references

Acknowledgments

This work is supported by the German Research Foundation (DFG) as part of the research project “PAK 357-Integrated Structural Health Monitoring in fibre composites through the examination of Lamb waves after excitation by piezoceramic plate actuators” which is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Institut für Mechanik, Helmut-Schmidt-Universität Hamburg, 22043, Hamburg, Germany

    B. Hennings & R. Lammering

  2. Institut für Mechanik, Otto-von-Guericke Universität Magdeburg, 39106, Magdeburg, Germany

    U. Gabbert

Authors
  1. B. Hennings
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Lammering
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. U. Gabbert
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. Hennings.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hennings, B., Lammering, R. & Gabbert, U. Numerical simulation of wave propagation using spectral finite elements. CEAS Aeronaut J 4, 3–10 (2013). https://doi.org/10.1007/s13272-012-0053-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13272-012-0053-9

Keywords

Search

Navigation