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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

has been cited by the following article:

• TITLE: Recursive Asymptotic Hybrid Matrix Method for Acoustic Waves in Multilayered Piezoelectric Media

  AUTHORS: Eng Leong Tan

  KEYWORDS: Hybrid Matrix Method, Recursive Asymptotic Method, Multilayered Media, Piezoelectric Media

  JOURNAL NAME: Open Journal of Acoustics, Vol.1 No.2, September 27, 2011

  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.