Relations between Transfer Matrices and Numerical Stability Analysis to Avoid the $\Omega d$ Problem

Article, Preprint English OPEN
Pérez-Álvarez, R.; Pernas-Salomón, R.; Velasco, V. R.;

The transfer matrix method is usually employed to study problems described by $N$ equations of matrix Sturm--Liouville (MSL) kind. In some cases a numerical degradation (the so called $\Omega d$ problem) appears thus impairing the performance of the method. We present h... View more
  • References (33)
    33 references, page 1 of 4

    [1] Yu Jiangong, Ding Juncai, and Ma Zhijuan. On dispersion relations of waves in multilayered magneto-electro-elastic plates. Applied Mathematical Modelling, 36(12):5780 - 5791, 2012.

    [2] YongQiang Guo, WeiQiu Chen, and YongLiang Zhang. Guided wave propagation in multilayered piezoelectric structures. Science in China Series G: Physics, Mechanics and Astronomy, 52(7):1094-1104, 2009.

    [3] H. Calas, R. Rodriguez-Ramos, J. A. Otero, L. Leija, A. Ramos, and G. Monsivais. Dispersion curves of shear horizontal wave surface velocities in multilayer piezoelectric systems. Journal of Applied Physics, 107(4):044511-044511-9, 2010.

    [4] R. P´erez-A´ lvarez and F. Garc´ıa-Moliner. Transfer Matrix, Green Function and related techniques: Tools for the study of multilayer heterostructures. Universitat Jaume I, Castello´n de la Plana, Spain, 2004.

    [5] J.W. Dunkin. Computation of modal solutions in layered, elastic media at high frequencies. Bulletin of the Seismological Society of America, 55(02):335-358., 1965.

    [6] S. I. Rokhlin and W. Huang. Ultrasonic wave interaction with a thin anisotropic layer between two anisotropic solids: Exact and asymptotic boundary condition methods. The Journal of the Acoustical Society of America, 92(3):1729-1742, 1992.

    [7] M.J.S. Lowe. Matrix techniques for modeling ultrasonic waves in multilayered media. Ultrasonics, Ferroelectrics, and Frequency Control, IEEE Transactions on, 42(4):525-542, July 1995.

    [8] S. I. Rokhlin and L. Wang. Stable recursive algorithm for elastic wave propagation in layered anisotropic media: Stiffness matrix method. The Journal of the Acoustical Society of America, 112(3):822-834, 2002.

    [9] Lugen Wang and S.I. Rokhlin. A compliance/stiffness matrix formulation of general green's function and effective permittivity for piezoelectric multilayers. Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on, 51(4):453-463, 2004.

    [10] Eng Leong Tan. Stiffness matrix method with improved efficiency for elastic wave propagation in layered anisotropic media. The Journal of the Acoustical Society of America, 118(6), 2005.

  • Metrics
Share - Bookmark