Perturbation Formulas for Polarization Ratio and Phase Shift of Rayleigh Waves in Prestressed Anisotropic Media

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.

Measurement of Lamb wave polarization using a one-dimensional scanning laser vibrometer (L)

“…Similar conclusions are reported in Ref. 11, where a perturbation approach is applied to consider an arbitrary state of surface stress. The literature on Lamb wave polarization is relatively more sparse and mostly limited to analytical and numerical studies.…”

“…[4][5][6] Investigations of Rayleigh waves polarization, for example, have studied its relation to the state of stress of a surface. [7][8][9][10][11] Specifically, the numerical investigation of Junge et al 10 have shown that surface stress has a much stronger effect on polarization than on phase velocity. Similar conclusions are reported in Ref.…”

Dispersion of Rayleigh waves in weakly anisotropic media with vertically-inhomogeneous initial stress

“…the methods in Sections 6 and 7 of Tanuma & Man (2002), Sections 6 and 7 of Tanuma & Man (2008), and Section 4 of Tanuma et al (2013)): …”

Perturbation of phase velocity of Rayleigh waves in pre-stressed anisotropic media with orthorhombic principal part

“…We will write ζ 22 , ζ 33 and ζ 23 − ζ 23 appearing in Equation (31) in terms of the entries of the matrices in (44) and the components Z ij in the formula (29). From (29) and (43) it follows that To investigate the effects of T • and A on the quantities above, we will look carefully at the components r 22 , r 33 and t 23 to show that the effects of T • and A on them come only from a 22 , a 23 , a 33 , a 44 and T • 22 , which proves the lemma.…”