Acoustic Waves in a Rotating Elastic Medium

Surface acoustic waves in rotating orthorhombic crystals

“…We see that even for small δ, this term plays an important role: for instance, the speed is reduced from 3409 m s −1 in the non-rotating case to 3350 m s −1 (horizontal dashed line) for δ = 0.088 52 with the full equations of motion, and for δ = 0.048 78 without the centripetal acceleration, a relative difference of 45% for the expected value of δ! Similarly, Grigor'evskiȋ et al . (2000) argued that one of the bulk waves disappeared in a rotating isotropic media at δ = 1 2 ; in fact, as shown by Schoenberg & Censor (1973), this phenomenon occurs at 'resonance': δ = Ω/ω = 1.…”

“…Clarke & Burdess (1994) obtained this equation for an isotropic half-space rotating about an axis orthogonal to the direction of propagation and to the normal to the half-space. Others (Lao 1980;Wauer 1999;Grigor'evskiȋ et al 2000;etc.) considered similar problems but neglected the centrifugal acceleration. For anisotropic crystals, Fang et al (2000) and Zhou & Jiang (2001) considered crystals of tetragonal symmetry but did not derive the secular equation explicitly.…”

“…Clarke & Burdess (1994) obtained this equation for an isotropic half-space rotating about an axis orthogonal to the direction of propagation and to the normal to the half-space. Others (see, for example, Lao 1980;Wauer 1999;Grigor'evskiȋ et al . 2000) considered similar problems but neglected the centrifugal acceleration.…”

Rayleigh Waves in Anisotropic Crystals Rotating About the Normal to a Symmetry Plane

“…Multiplying this equality to the left by a R T = q T A T and to the right by q, and using Eqs. (7), (8), we conclude that (see [20] for the non-rotating case),…”

“…1). The secular equation for rotating materials was obtained by others but in simpler settings: by Clarke and Burdess in an isotropic material, first for small rotation rate/wave frequency ratios [4], then for any ratio [5]; by Grigor'evskiȋ, Gulyaev, and Kozlov [7] also for isotropic materials but neglecting the centrifugal force; and by Fang, Yang, and Jiang [6] for crystals having tetragonal symmetry. Here, the analysis is fully developed for crystals with a single symmetry plane, up to the derivation of the secular equation in explicit form, that is an equation giving the Rayleigh wave speed in terms of the elastic parameters and of the rotation rate.…”