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

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.

[1]  J. Rose Ultrasonic Waves in Solid Media , 1999 .

[2]  M.J.S. Lowe,et al.  Matrix techniques for modeling ultrasonic waves in multilayered media , 1995, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[3]  Peter Cawley,et al.  A 2-dimensional Fourier transform method for the quantitative measurement of Lamb modes , 1990, IEEE Symposium on Ultrasonics.

[4]  C. Prada,et al.  Laser-based ultrasonic generation and detection of zero-group velocity Lamb waves in thin plates , 2005 .

[5]  Eduardo Kausel,et al.  Wave propagation in anisotropic layered media , 1986 .

[6]  Rolf Lammering,et al.  Investigation on piezoelectrically induced Lamb wave generation and propagation , 2007 .

[7]  F. Harris On the use of windows for harmonic analysis with the discrete Fourier transform , 1978, Proceedings of the IEEE.

[8]  T. Sarkar,et al.  Using the matrix pencil method to estimate the parameters of a sum of complex exponentials , 1995 .

[9]  Barry T. Smith,et al.  Time-frequency analysis of the dispersion of Lamb modes. , 1999, The Journal of the Acoustical Society of America.

[10]  Victor Giurgiutiu,et al.  7 – PIEZOELECTRIC WAFER ACTIVE SENSORS , 2008 .

[11]  Sébastien Grondel,et al.  The propagation of Lamb waves in multilayered plates: phase-velocity measurement , 1999 .

[12]  Tapan K. Sarkar,et al.  Matrix pencil method for estimating parameters of exponentially damped/undamped sinusoids in noise , 1990, IEEE Trans. Acoust. Speech Signal Process..

[13]  J. Achenbach Wave propagation in elastic solids , 1962 .

[14]  F. Schöpfer,et al.  A Mathematical Analysis of the Strip-Element Method for the Computation of Dispersion Curves of Guided Waves in Anisotropic Layered Media , 2010 .

[15]  Ramón Abascal,et al.  Numerical simulation of Lamb wave scattering in semi‐infinite plates , 2001 .