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Stable recursive algorithm for elastic wave propagation in layered anisotropic media: stiffness matrix method.

S I Rokhlin1, L Wang

  • 1The Ohio State University, Nondestructive Evaluation Program, Edison Joining Technology Center, Columbus 43221, USA. rokhlin.2@osu.edu

The Journal of the Acoustical Society of America
|September 24, 2002
PubMed
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A new stiffness matrix method efficiently models wave propagation in anisotropic multilayered media. This stable, recursive algorithm is suitable for complex composite materials and various wave types.

Area of Science:

  • * Computational physics and materials science.
  • * Acoustics and wave propagation.
  • * Solid mechanics and composite materials.

Background:

  • * Modeling wave propagation in multilayered anisotropic media presents computational challenges.
  • * Existing methods like the transfer matrix method can face stability issues at high frequencies or for thick layers.
  • * Efficient and stable algorithms are needed for analyzing complex layered materials.

Purpose of the Study:

  • * To develop an efficient and unconditionally stable recursive algorithm for wave propagation analysis.
  • * To introduce the stiffness matrix method for multilayered anisotropic media.
  • * To adapt the method for periodic structures like composites and analyze specific wave phenomena.

Main Methods:

Related Experiment Videos

  • * Development of a recursive stiffness matrix method.
  • * Calculation of stiffness (compliance) matrices for individual layers and recursive application to layered systems.
  • * Computation of reflection and transmission coefficients for layered media bounded by semispaces.

    • Main Results:

    • * The stiffness matrix method demonstrates unconditional computational stability for high frequency and layer thickness.
    • * The algorithm's computation time is proportional to the number of layers, offering efficiency.
    • * The method accurately models wave propagation in periodic structures and determines characteristic equations for Lamb and Floquet waves.

    Conclusions:

    • * The stiffness matrix method provides an efficient, stable, and adaptable approach for wave propagation in multilayered anisotropic media.
    • * The algorithm's stability and efficiency make it suitable for analyzing complex layered systems, including composites.
    • * The method successfully models phenomena like angle beam pulse reflections and characteristic wave equations in periodic media.