Advertisement

A Minimal Model for Fast Approximation of Lamb Wave Propagation in Complex Aircraft Parts

  • C. Heinze
  • S. Duczek
  • M. SinapiusEmail author
Chapter
Part of the Research Topics in Aerospace book series (RTA)

Abstract

For future integrated structural health monitoring (SHM) systems the complexity of the used algorithms is limited due to the restricted computational capacities of the onboard CPU. Therefore, an efficient method to approximate the wave propagation in complex fiber reinforced polymer structures is proposed. Model properties are reduced to phase velocities in individual areas and interaction characteristics at their connecting spots. A ray tracing algorithm enables a fast identification of possible wave paths from an actuator to a sensor. With this information, signals at the sensor position can be calculated analytically. The accuracy of this method is checked on an aluminum plate with and without a cutout. The present chapter is concluded with a discussion of advantages and limitations of the proposed method and an outlook to its use for anisotropic materials.

References

  1. 1.
    Ahmad ZAB (2011) Numerical simulation of lamb waves in plates using a semi-analytical finite element method. VDI Fortschritt-Berichte Reihe 20 Nr. 437Google Scholar
  2. 2.
    Ahmad ZAB, Vivar-Perez JM, Gabbert U (2013) Semi-analytical finite element method for modeling of lamb wave propagation. CEAS Aeronaut J 4:21–33CrossRefGoogle Scholar
  3. 3.
    Baaran J (2010) Grundlagenuntersuchungen zur Ausbreitung von Lambwellen in Hybrid-laminaten. Internal report. German Aerospace Center (DLR) – Institute of Composite Structures and Adaptive Systems, IB 131-2010/45Google Scholar
  4. 4.
    Bleistein N, Cohen JK, Stockwell JW Jr (2013) Mathematics of multidimensional seismic imaging, migration, and inversion, vol 13. Springer Science and Business Media, New YorkzbMATHGoogle Scholar
  5. 5.
    Chapuis B, Terrien N, Royer D (2011) Modeling and experimental investigations of Lamb waves focusing in anisotropic plates. J Phys: Conf Ser 269:1–8Google Scholar
  6. 6.
    Croxford AJ, Moll J, Wilcox PD, Michaels JE (2010) Efficient temperature compensation strategies for guided wave structural health monitoring. Ultrasonics 50(4):517–528CrossRefGoogle Scholar
  7. 7.
    Dolinskaya IS, Smith RL (2013) Fastest-path planning for direction-dependent speed functions. J Optim Theory Appl 158(2):480–497MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Duczek S, Joulaian M, Düster A, Gabbert U (2013) Simulation of Lamb waves using the spectral cell method. In: SPIE smart structures and materials + nondestructive evaluation and health monitoring. International Society for Optics and Photonics, Bellingham, pp 86,951U–86,951UGoogle Scholar
  9. 9.
    Eckstein B, Moix-Bonet M, Bach M (2014) Analysis of environmental and operational condition effects on guided ultrasonic waves in stiffened CFRP structures. In: Le Cam V, Mevel L, Schoefs F (eds) EWSHM - 7th European workshop on structural health monitoring, IFFSTTAR, Inria, Université de Nantes, Nantes, FranceGoogle Scholar
  10. 10.
    Fahy FJ, Gardonio P (2007) Sound and structural vibration: radiation, transmission and response. Academic, AmsterdamGoogle Scholar
  11. 11.
    Gravenkamp H, Song C, Prager J (2012) A numerical approach for the computation of dispersion relations for plate structures using the scaled boundary finite element method. J Sound Vib 331(11):2543–2557CrossRefGoogle Scholar
  12. 12.
    Gravenkamp H, Birk C, Song C (2015) Simulation of elastic guided waves interacting with defects in arbitrarily long structures using the scaled boundary finite element method. J Comput Phys 295:438–455MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Greve DW, Neumann JJ, Nieuwenhuis JH, Oppenheim IJ, Tyson NL (2005) Use of Lamb waves to monitor plates: experiments and simulations. In: Smart structures and materials. International Society for Optics and Photonics, Bellingham, pp 281–292Google Scholar
  14. 14.
    Griffiths DJ (1999) Introduction to electrodynamics, 3rd edn. Prentice Hall, Upper Saddle River, NJGoogle Scholar
  15. 15.
    Heinze C (2011) Auslegung von modenselektiven Aktuatoren zur Anregung von Lambwellen in Faserverbundplatten. Diplomarbeit, Otto-von-Guericke-Universität Magdeburg, MagdeburgGoogle Scholar
  16. 16.
    Hennings B, Lammering R, Gabbert U (2013) Numerical simulation of wave propagation using spectral finite elements. CEAS Aeronaut J 4(1):3–10CrossRefGoogle Scholar
  17. 17.
    Kijanka P, Radecki R, Packo P, Staszewski WJ, Uhl T (2013) GPU-based local interaction simulation approach for simplified temperature effect modelling in Lamb wave propagation used for damage detection. Smart Mater Struct 22(3):035014CrossRefGoogle Scholar
  18. 18.
    Liu GR, Quek Jerry SS (2003) A non-reflecting boundary for analyzing wave propagation using the finite element method. Finite Elem Anal Des 39(5):403–417CrossRefGoogle Scholar
  19. 19.
    Neumann MN, Hennings B, Lammering R (2014) Quasi-continuous mode conversion of Lamb waves in CFRP plates due to inhomogeneity on Micro and Meso scale. In: EWSHM – 7th European workshop on structural health monitoring, Nantes, FranceGoogle Scholar
  20. 20.
    Rahman MU, Prager J (2012) Simulating the sound propagation of guided waves using the Elastodynamic Finite Integration Technique (EFIT). 6th European workshop on structural health monitoring, pp 1–6Google Scholar
  21. 21.
    Schmidt D (2014) Modenselektive Übertragung von Lambwellen in Faserverbundstrukturen. PhD thesis, Technische Universität Carolo-Wilhelmina zu Braunschweig, DLR-ForschungsberichtGoogle Scholar
  22. 22.
    Schmidt D, Sadri H, Szewieczek A, Sinapius M, Wierach P, Siegert I, Wendemuth A (2013) Characterization of Lamb wave attenuation mechanisms. In: SPIE smart structures and materials + nondestructive evaluation and health monitoring, vol 8695Google Scholar
  23. 23.
    Schmidt D, Wierach P, Sinapius M (2014) Mode selective actuator-sensor system for Lamb wave-based structural health monitoring. In: EWSHM – 7th European workshop on structural health monitoring, Nantes, FranceGoogle Scholar
  24. 24.
    Schubert KJ, Brauner C, Hermann A (2013) Non-damage related influences on Lamb wave based SHM of CFRP structures. Struct Health Monit 13(2):158–176CrossRefGoogle Scholar
  25. 25.
    Smith SW (1997) The Scientist and Engineer’s guide to digital signal processing. California Technical Publications, San DiegoGoogle Scholar
  26. 26.
    Viktorov IA (1967) Rayleigh and Lamb waves: physical theory and applications. Plenum Press, New YorkCrossRefGoogle Scholar
  27. 27.
    Vivar-Perez JM (2014) Hybrid analytical-spectral method for the modeling of piezoelectrically induced waves in plates. In: EWSHM – 7th European workshop on structural health monitoring, Nantes, FranceGoogle Scholar
  28. 28.
    Wilcox P (1998) Lamb wave inspection of large structures using permanently attached transducers. PhD thesis, Imperial College of Science, Technology, and Medicine, Mechanical Engineering Department, University of LondonGoogle Scholar
  29. 29.
    Willberg C, Gabbert U (2012) Development of a three-dimensional piezoelectric isogeometric finite element for smart structure applications. Acta Mech 223(8):1837–1850MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Willberg C, Duczek S, Vivar-Perez JM, Schmicker D, Gabbert U (2012) Comparison of different higher order finite element schemes for the simulation of Lamb waves. Comput Methods Appl Mech Eng 241:246–261CrossRefzbMATHGoogle Scholar
  31. 31.
    Wölcken PC, Papadopoulos M (2015) Smart intelligent aircraft structures (SARISTU): proceedings of the final project conference. Springer International Publishing, ChamGoogle Scholar
  32. 32.
    Yu L, Leckey CAC, Tian Z (2013) Study on crack scattering in aluminum plates with Lamb wave frequency–wavenumber analysis. Smart Mater Struct 22(6):065019CrossRefGoogle Scholar
  33. 33.
    Zhao X, Gao H, Zhang G, Ayhan B, Yan F, Kwan C, Rose JL (2007) Active health monitoring of an aircraft wing with embedded piezoelectric sensor/actuator network: I. Defect detection, localization and growth monitoring. Smart Mater Struct 16(4):1208–1217CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.German Aerospace Center (DLR)Institute of Composite Structures and Adaptive SystemsHamburgGermany
  2. 2.Institute of Mechanics, Otto von Guericke University MagdeburgMagdeburgGermany
  3. 3.Institute of Adaptronics and Function IntegrationBraunschweig University of TechnologyBraunschweigGermany

Personalised recommendations