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Accurate determination of dispersion curves of guided waves in plates by applying the matrix pencil method to laser vibrometer measurement data

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Abstract

Accurate knowledge of the dispersion relations of guided waves in plates is important for the efficient use of Lamb wave-based damage-detection methods. In this paper, we introduce a method which aims at automatically extracting the dispersion curves from laser vibrometer measurement data in an easy and robust manner. This method works by Fourier transforming the measurement data into the wavenumber domain and then applying the matrix pencil method by Hua and Sarkar to extract the wavenumber-dependent frequencies. As an additional result, we are able to experimentally detect backward propagating waves in aluminium plates.

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References

  1. Achenbach, J.D.: Wave Propagation in Elastic Solids. North-Holland, Amsterdam (1973)

    MATH  Google Scholar 

  2. Alleyne, D., Cawley, P.: A 2-dimensional Fourier transform method for the quantitative measurement of Lamb modes. In: Ultrasonics Symposium, 1990. Proceedings, IEEE 1990, vol. 2, pp. 1143–1146 (1990) doi:10.1109/ULTSYM.1990.171541

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

    Article  Google Scholar 

  4. Galan, J.M., Abascal, R.: Numerical simulation of Lamb wave scattering in semi-infinite plates. Int. J. Numer. Methods. Eng. 53, 1145–1173 (2002). doi:10.1002/nme.331

    Article  Google Scholar 

  5. Giurgiutiu, V.: Structural Health Monitoring with Piezoelectric Wafer Active Sensors. Academic Press, Amsterdam, Boston (2008)

  6. Grondel, S., Assaad, J., Delebarre, C., Blanquet, P., Moulin, E.: The propagation of Lamb waves in multilayered plates: phase-velocity measurement. Meas. Sci. Technol. 10, 348–353 (1999). doi:10.1088/0957-0233/10/5/002

    Article  Google Scholar 

  7. Harris, F.J.: On the use of windows for harmonic analysis with the discrete Fourier transform. Proc. IEEE 66, 51–83 (1978)

    Article  Google Scholar 

  8. Hua, Y., Sarkar, T.: Matrix pencil method for estimating parameters of exponentially damped/undamped sinusoids in noise. IEEE Trans. Acoust. Speech Signal Process. 38(5), 814–824 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kausel, E.: Wave propagation in anisotropic layered media. Int. J. Numer. Methods. Eng. 23, 1567–1578 (1986)

    Article  MATH  Google Scholar 

  10. Lowe, M.J.S.: Matrix techniques for modeling ultrasonic waves in multilayered media. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 42(4), 525–542 (1995)

    Article  Google Scholar 

  11. Prada, C., Balogun, O., Murray, T.W.: Laser-based ultrasonic generation and detection of zero-group velocity Lamb waves in thin plates. Appl. Phys. Lett. 87. (2005) doi:10.1063/1.2128063

  12. Prosser, W.H., Seale, M.D., Smith, B.T.: Time-frequency analysis of the dispersion of Lamb modes. J. Acoust. Soc. Am. 105(5), 2669–2676 (1999)

    Article  Google Scholar 

  13. Rose, J.: Ultrasonic Waves in Solid Media. Cambridge University Press, New York (1999)

  14. Sarkar, T.K., Pereira, O.: Using the matrix pencil method to estimate the parameters of a sum of complex exponentials. IEEE Antennas Propag. Mag. 37(1), 48–55 (1995)

    Article  Google Scholar 

  15. Schöpfer, F., Binder, F., Wöstehoff, A., Schuster, T.: A mathematical analysis of the strip element method for the computation of dispersion curves of guided waves in anisotropic layered media. Math. Probl. Eng. 22, 311–329 (2010)

    Google Scholar 

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Acknowledgments

The work of F. Binder and T. Schuster is being supported by Deutsche Forschungsgemeinschaft (DFG) under Schu 1978/4-1.

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Authors and Affiliations

  1. Institut für Mathematik, Carl von Ossietzky Universität, 26111, Oldenburg, Germany

    F. Schöpfer & T. Schuster

  2. Fakultät für Maschinenbau, Helmut-Schmidt-Universität, 22043, Hamburg, Germany

    F. Binder, A. Wöstehoff, S. von Ende, S. Föll & R. Lammering

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  1. F. Schöpfer
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  2. F. Binder
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  3. A. Wöstehoff
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  4. T. Schuster
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  5. S. von Ende
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  6. S. Föll
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  7. R. Lammering
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Correspondence to F. Schöpfer.

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Schöpfer, F., Binder, F., Wöstehoff, A. et al. Accurate determination of dispersion curves of guided waves in plates by applying the matrix pencil method to laser vibrometer measurement data. CEAS Aeronaut J 4, 61–68 (2013). https://doi.org/10.1007/s13272-012-0055-7

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  • DOI: https://doi.org/10.1007/s13272-012-0055-7

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