Finite Element Analysis in Combination with Perfectly Matched Layer to the Numerical Modeling of Acoustic Devices in Piezoelectric Materials


The characterization of finite length Surface Acoustic Wave (SAW) and Bulk acoustic Wave (BAW) resonators is addressed here. The Finite Element Analysis (FEA) induces artificial wave reflections at the edges of the mesh. In fact, these ones do not contribute in practice to the corresponding experimental response. The Perfectly Matched Layer (PML) method, allows to suppress the boundary reflections. In this work, we first demonstrate the basis of PML adapted to FEA formalism. Next, the results of such a method are depicted allowing a discussion on the behavior of finite acoustic resonators.

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D. Karim, S. Ballandras, T. Laroche, K. Wagner, J. Brice and X. Perois, "Finite Element Analysis in Combination with Perfectly Matched Layer to the Numerical Modeling of Acoustic Devices in Piezoelectric Materials," Applied Mathematics, Vol. 4 No. 5A, 2013, pp. 64-71. doi: 10.4236/am.2013.45A008.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] M. Solal, S. Ballandras and V. Laud, “A P-Matrix Based Model for SAW Grating Waveguides Taking into Account Modes Conversion at the Reflection,” IEEE Transactions on UFFC, Vol. 51, No. 12, 2004, pp. 1690-1696.
[2] T. Laroche, M. Mayer, X. Perois, W. Daniau, J. Garcia, S. Ballandras and K. Wagner, “Mixed Finite Element Analysis/Boundary Element Method Based on Canonical Green’s Function to Address Non-Periodic Acoustic Devices,” 2011 Proceeding of Ultrasonics Symposium (IUS), Orlan do, 2011, pp. 1850-1853.
[3] J. P. Bérenger, “A Perfectly Matched Layer for the Absorption of Electromagnetic Wave,” Journal of Computational Physics, Vol. 114, No. 2, 1994, pp. 185-200. doi:10.1006/jcph.1994.1159
[4] D. Komatitsch and J. Tromp, “A Perfectly Matched Layer Absorbing Boundary Condition for the Second-Order Seismic Wave Equation,” Geophysical Journal International, Vol. 154, No. 1, 2003, pp. 146-153. doi:10.1046/j.1365-246X.2003.01950.x
[5] Y. B. Zheng and X. J. Huang, “Anisotropic Perfectly Matched Layers for Elastic Waves in Cartesian and Curvilinear Coordinates,” MIT Earth Resources Laboratory Industry Consortium Report, Massachusetts Institute of Technology, Earth Resources Laboratory, 2002.
[6] D. Appel?, “Absorbing Layers and Non-Reflecting Boundary Conditions for Wave Propagation Problems,” Ph.D. Thesis, KTH Royal Institute of Technology, Stockholm, 2005.
[7] H. F. Tiersten, “Hamilton’s Principle for Linear Piezo electric Media,” Proceedings of the IEEE, Vol. 55, No. 8, 1967, pp. 1523-1524.
[8] E. P. Eernisse, “Variationnal Method for Electroelastic Vibration Analysis,” IEEE Transactions on Sonics and Ultrasonics, Vol. 14, No. 4, 1967, pp. 153-160. doi:10.1109/T-SU.1967.29431
[9] H. Allik and T. J. R. Hugues, “Finite Element Method for Piezoelectric Vibration,” International Journal for Numerical Methods in Engineering, Vol. 2, No. 2, 1970, pp. 151-157. doi:10.1002/nme.1620020202
[10] H. Allik, K. M. Webman and J. T. Hunt, “Vibrational Response of Sonar Transducers Using Piezoelectric Finite Elements,” Journal of the Acoustical Society of America, Vol. 56, No. 6, 1974, pp. 1782-1791. doi:10.1121/1.1903513
[11] D. Boucher, Y. Lagier and C. Maerfeld, “Computation of the Vibrationnal Modes for Piezoelectric Transducers Using a Mixed Finite Element Pertubational Method,” IEEE Transactions on Sonics and Ultrasonics, Vol. 28, No. 5, 1981, pp. 318-330. doi:10.1109/T-SU.1981.31270
[12] M. Naillon, R. H. Coursant and F. Besnier, “Analyse de Structures Piézoélectriques par une Méthode des éléments Finis,” Acta Electronica, Vol. 25, No. 4, 1983, pp. 341-362.
[13] W. Steichen, G. Vanderbork and Y. Lagier, “Determination of the Power Limits of a High Frequency Transducer Using the Finite Element Method,” Power Sonic and Ultrasonic Transducers Design, 1988, pp.160-174.
[14] R. Lerch, “Simulation of Piezoelectric Devices by Two and Three Dimensionnal Finite Elements,” IEEE Trans actions on Ultrasonics, Ferroelectrics and Frequency Control, Vol. 37, No. 3, 1990, pp. 233-247. doi:10.1109/58.55314

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