Guided waves in anisotropic layers: the low-frequency limits

The low-frequency limiting velocities of guided waves propagating in homogeneous layers with the traction-free boundary conditions and arbitrary elastic anisotropy are analyzed by constructing the secular equation based on Cauchy sextic formalism coupled with the low-frequency asymptotic analysis. T...

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Bibliographic Details
Published in:Acta mechanica 2022-12, Vol.233 (12), p.5255-5263
Main Author: Kuznetsov, S. V.
Format: Article
Language:English
Subjects:
Acoustics
Anisotropy
Asymptotic methods
Boundary conditions
Classical and Continuum Physics
Constraining
Control
Decomposition
Dynamical Systems
Eigenvalues
Elastic analysis
Elastic anisotropy
Elastic limit
Engineering
Engineering Fluid Dynamics
Engineering Thermodynamics
Free boundaries
Frequency analysis
Heat and Mass Transfer
Mathematical analysis
Original Paper
Solid Mechanics
Tensors
Theoretical and Applied Mechanics
Velocity
Vibration
Wave propagation
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Description
Summary:The low-frequency limiting velocities of guided waves propagating in homogeneous layers with the traction-free boundary conditions and arbitrary elastic anisotropy are analyzed by constructing the secular equation based on Cauchy sextic formalism coupled with the low-frequency asymptotic analysis. The combined method allows us constructing a closed form solution in terms of the eigenvalues of a three-dimensional auxiliary matrix (tensor) composed of convolutions of the elasticity tensor with the unit normal to the median plane and the wave vector. The performed analytical and numerical studies reveal (i) coinciding (up to a multiplier) the set of admissiblelimiting velocities with the spectral set of an auxiliary matrix; (ii) degeneracy of the constructed auxiliary matrix at any elastic anisotropy; and (iii) presence of no more than two low-frequency limiting velocities (not necessarily distinct) at any kind of elastic anisotropy.
ISSN:0001-5970
1619-6937
DOI:10.1007/s00707-022-03375-4