Recursive Asymptotic Hybrid Matrix Method for Acoustic Waves in Multilayered Piezoelectric Media
- 1
Abstract
This paper presents the recursive asymptotic hybrid matrix method for acoustic waves in multilayered piezoelectric media. The hybrid matrix method preserves the numerical stability and accuracy across large and small thicknesses. For discussion and comparison, the scattering matrix method is also presented in physics-based form and coherent form. The latter form resembles closely that of hybrid matrix method and helps to highlight their relationship and distinction. For both scattering and hybrid matrix methods, their formulations in terms of eigenwaves solution are provided concisely. Making use of the hybrid matrix, the recursive asymptotic method without eigenwaves solution is described and discussed. The method bypasses the intricacies of eigenvalue-eigenvector approach and requires only elementary matrix operations along with thin- layer asymptotic approximation. It can be used to determine Green’s function matrix readily and facilitates the trade-off between computation efficiency and accuracy.
- E. L. Adler, “Matrix Methods Applied to Acoustic Waves in Multilayers,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, Vol. 37, No. 6, 1990, pp. 485-490. doi:10.1109/58.63103
- B. Collet, “Recursive Surface Impedance Matrix Methods for Ultrasonic Wave Propagation in Piezoelectric Multilayers,” Ultrasonics, Vol. 42, No. 1-9, 2004, pp. 189-197.
- L. Wang and S. I. Rokhlin, “A Compliance/Stiffness Matrix Formulation of General Green’s Function and Effective Permittivity for Piezoelectric Multilayers,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, Vol. 51, No. 4, 2004, pp. 453-463.
- E. L. Tan, “Stiffness Matrix Method with Improved Efficiency for Elastic Wave Propagation in Layered Anisotropic Media,” Journal of the Acoustical Society of America, Vol. 118, No. 6, 2005, pp. 3400-3403. doi:10.1121/1.2118287
- E. L. Tan, “A Robust Formulation of SAW Green’s Functions for Arbitrarily Thick Multilayers at High Frequencies,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, Vol. 49, No. 7, 2002, pp. 929- 936. doi:10.1109/TUFFC.2002.1020163
- E. L. Tan, “A Concise and Efficient Scattering Matrix Formalism for Stable Analysis of Elastic Wave Propagation in Multilayered Anisotropic Solids,” Ultrasonics, Vol. 41, No. 3, 2003, pp. 229-236. doi:10.1016/S0041-624X(02)00447-X
- T. Pastureaud, V. Laude, and S. Ballandras, “Stable Scatteringmatrix Method for Surface Acoustic Waves in Piezoelectric Multilayers,” Applied Physics Letters, Vol. 80, No. 14, 2002, pp. 2544-2546. doi:10.1063/1.1467620
- E. L. Tan, “Hybrid Compliance-Stiffness Matrix Method for Stable Analysis of Elastic Wave Propagation in Multilayered Anisotropic Media,” Journal of the Acoustical Society of America, Vol. 119, No. 1, 2006, pp. 45-53. doi:10.1121/1.2139617
- E. L. Tan, “Matrix Algorithms for Modeling Acoustic Waves in Piezoelectric Multilayers,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, Vol 54, No. 10, 2007, pp. 2016-2023. doi:10.1109/TUFFC.2007.496
- V. Y. Zhang and V. Laude, “Unified and Stable Scattering Matrix Formalism for Acoustic Waves in Piezoelectric Stacks,” Journal of Applied Physics, Vol. 104, 2008, 064916.
- M. Lam, E. Le Clézio, H. Amorín, M. Algueró, Janez Holc, Marija Kosec, A. C. Hladky-Hennion and G. Feuillard, “Acoustic Wave Transmission through Piezoelectric Structured Materials,” Ultrasonics, Vol. 49, No. 4-5, 2009, pp. 424-431.