Authors:
M. S. L. R. Mallika,G. Sudheer,N. Aparna,DOI NO:
https://doi.org/10.26782/jmcms.2026.08.00014Keywords:
guided waves; cortical bone; quantitative ultrasound; spectral collocation; transverse isotropy; elastic materials with voids,Abstract
Bone quantitative ultrasound (QUS) relies on the dispersion of guided waves propagating in the cortical shell of long bones. Analytical fluid–solid–fluid trilayer models obtain the dispersion relation from a characteristic determinant whose roots must be located numerically, a procedure that becomes delicate near mode osculations and for anisotropic cortical bone. Here the fluid–solid–fluid waveguide is reformulated as a linear generalized eigenvalue problem using a Chebyshev spectral-collocation method. Each layer is discretized on a Chebyshev–Gauss–Lobatto grid, and the interface and free-surface conditions are imposed directly by row replacement. For a prescribed wavenumber, the eigenvalue is W = ω², so every finite discrete eigenmode follows from a single generalized eigensolve without determinant root searching; the physical guided branches are then selected by explicit admissibility and participation criteria. The method is validated against an independently implemented analytical global-matrix solver for a water/aluminum/water trilayer: the fundamental extensional (S₀) and flexural (A₀) phase velocities agree within numerical tolerance (better than 10⁻⁵ %), and a convergence study with eigen-residual norms confirms spectral accuracy at about fourteen collocation nodes per layer. The same framework is then extended to a transversely isotropic cortical-bone layer and, with one additional volume-fraction field, to a linear elastic material with voids. Transverse isotropy raises the low-frequency extensional plateau by about 8.2 %, whereas increasing void coupling lowers it by up to 15 %. A Hellmann–Feynman sensitivity analysis shows that this plateau constrains only one stiffness combination, so these figures are forward-model discrepancies rather than uniquely recoverable inverse biases.Refference:
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