Perturbation Formulas for Polarization Ratio and Phase Shift of Rayleigh Waves in Prestressed Anisotropic Media |
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Authors: | Kazumi Tanuma Chi-Sing Man |
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Institution: | (1) Department of Mathematics, Graduate School of Engineering, Gunma University, Kiryu 376-8515, Japan;(2) Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, USA |
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Abstract: | This paper completes an earlier study (Tanuma and Man, Journal of Elasticity, 85, 21–37, 2006) where we derive a first-order perturbation formula for the phase velocity of Rayleigh waves that propagate along the free
surface of a macroscopically homogeneous, anisotropic, prestressed half-space. We adopt the formulation of linear elasticity
with initial stress and assume that the deviation of the prestressed anisotropic medium from a suitably-chosen, comparative,
unstressed and isotropic state be small. No assumption, however, is made on the material anisotropy of the incremental elasticity
tensor. With the help of the Stroh formalism, here we derive first-order perturbation formulas for the changes in polarization
ratio and phase shift of Rayleigh waves from their respective comparative isotropic value. Examples are given, which show
that the perturbation formulas for phase velocity and polarization ratio can serve as a starting point for investigations
on the possible advantages of using Rayleigh-wave polarization, as compared with using wave speed, for acoustoelastic measurement
of stress.
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Keywords: | Rayleigh waves Prestressed anisotropic media Polarization ratio Phase shift Stroh formalism Nondestructive evaluation |
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