GEW piezo plate

Script to compute guided waves in piezoelectric plates.

https://github.com/dakiefer/gewpiezoplate

GEW piezo plate is a minimal script for fast and robust computation of guided electroelastic waves in piezoelectric plates. It implements the spectral collocation method (SCM) based on DMSUITE and is an extension to GEW dispersion script. The code implements the method from

D. A. Kiefer, G. Watzl, K. Burgholzer, M. Ryzy, and C. Grünsteidl, “Electroelastic guided wave dispersion in piezoelectric plates: Spectral methods and laser-ultrasound experiments,” Journal of Applied Physics, vol. 137, no. 11, p. 114502, Mar. 2025, 10.1063/5.0250494.

Features:

• only ~100 comprehensive lines of Matlab code
• electrically "shorted" or "open" plate surfaces
• arbitrary propagation direction

Piezoelectricity couples the mechanical displacement vector u to the electrostatic potential φ. We solve for these fields across the plate thickness as depicted in the figure below.

Computational results are depicted below in the form of dispersion curves. The wave field of three selected modes are also shown.

[!TIP] This is a simple script that should be easy to extend with custom functionality. If you are rather looking for a full system to compute and postprocess guided waves, have a look at GEWtool.

How to use

1. Change into the GEW_piezo_plate folder or add it to the Matlab path.
2. Execute plate_piezoelectric_SCM.m . Enjoy!

How to cite

If this code is useful to you, please cite the accompanying paper:

D. A. Kiefer, G. Watzl, K. Burgholzer, M. Ryzy, and C. Grünsteidl, “Electroelastic guided wave dispersion in piezoelectric plates: Spectral methods and laser-ultrasound experiments,” Journal of Applied Physics, vol. 137, no. 11, p. 114502, Mar. 2025, 10.1063/5.0250494.

as well as the software itself:

D. A. Kiefer and C. Grünsteidl (2024). GEW piezo plate. https://doi.org/10.5281/zenodo.14205789 (https://github.com/dakiefer/GEWpiezoplate)

Dependencies

This software bundles chebdif.m from DMSUITE:

J.A.C Weideman (2022). DMSUITE (https://www.mathworks.com/matlabcentral/fileexchange/29-dmsuite), MATLAB Central File Exchange. Retrieved August 18, 2022.

Literature

[1] D. A. Kiefer, G. Watzl, K. Burgholzer, M. Ryzy, and C. Grünsteidl, “Electroelastic guided wave dispersion in piezoelectric plates: Spectral methods and laser-ultrasound experiments,” Journal of Applied Physics, vol. 137, no. 11, p. 114502, Mar. 2025, 10.1063/5.0250494.
[2] L. N. Trefethen, Spectral Methods in MATLAB. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2000. doi: 10.1137/1.9780898719598.
[3] J. A. Weideman and S. C. Reddy, “A MATLAB Differentiation Matrix Suite,” ACM Trans. Math. Softw., vol. 26, no. 4, pp. 465–519, Dec. 2000, doi: 10.1145/365723.365727.
[4] A. T. I. Adamou and R. V. Craster, “Spectral methods for modelling guided waves in elastic media,” The Journal of the Acoustical Society of America, vol. 116, no. 3, pp. 1524–1535, Sep. 2004, doi: 10.1121/1.1777871.
[5] B. A. Auld, Acoustic Fields and Waves in Solids, 2nd ed., vol. 2. Malabar: Krieger Publishing Company, 1990.
[6] H. F. Tiersten, “Wave Propagation in an Infinite Piezoelectric Plate,” The Journal of the Acoustical Society of America, vol. 35, no. 2, pp. 234–239, Feb. 1963, doi: 10.1121/1.1918438.
[7] J. E. Lefebvre, V. Zhang, J. Gazalet, and T. Gryba, “Conceptual advantages and limitations of the Laguerre polynomial approach to analyze surface acoustic waves in semi-infinite substrates and multilayered structures,” Journal of Applied Physics, vol. 83, no. 1, pp. 28–34, Jan. 1998, doi: 10.1063/1.366697.
[8] D. A. Kiefer, Elastodynamic quasi-guided waves for transit-time ultrasonic flow metering, ser. FAU Forschungen, Reihe B, Medizin, Naturwissenschaft, Technik, vol. 42. Erlangen: FAU University Press, 2022, doi: 10.25593/978-3-96147-550-6.

Authors

Code created 2024 by:

Daniel A. Kiefer, Institut Langevin, ESPCI Paris, Université PSL, France
Contact: daniel.kiefer@espci.fr   •   dakiefer.net   •   Follow me on ResearchGate!
            

Clemens Grünsteidl, Research Center for Non Destructive Testing GmbH, Austria
Contact: clemens.gruensteidl@recendt.at   •   Follow me on ResearchGate!