The Behaviour of Elastic Surface Waves Polarized in a Plane of Material Symmetry. I. Addendum
D. M. Barnett, P. Chadwick, J. Lothe
1991
Proceedings of the Royal Society A
Proc. R. Soc. Lond. A (1991) 433, 699-710 Printed in Great Britain 699 700 D. M. Barnett, P. Chadwick and Lothe in configurations in which R does not coincide with a plane of m aterial sym m etry and which also adm it a subsonic surface wave. Unlike symmetric surface waves, the secluded type of supersonic wave is not a pure mode. The analysis of Gundersen et al. (1991) stems from an earlier investigation by Alshits & Lothe (1981) of the reflection of homogeneous plane waves a t the tractionfree
more »
... boundary of a semi-infinite anisotropic elastic body. Alshits & Lothe (1981, p. 304) introduced the space of simple reflection consisting of all speed-configuration pairs {v, W) with the property th a t there exist in ^ homogeneous plane waves with slowness vectors si and sr such th a t si e1 = and reflected waves in a simple reflection effect a t the boundary. (The unit vector e1 is in R and along the bou n d ary : the configuration is the orientation of the elements of material sym m etry relative to the basis {e1,e 2,e 3}, x I t was proved by Alshits & Lothe (1981, §4) th a t the speed of propagation and the configuration adm itting a two-component supersonic surface wave necessarily belong to 01 and on this basis Gundersen et al. (1991) searched for secluded supersonic surface waves within the appropriate subspace of 0 . I t is desirable th a t the theory of supersonic surface waves, as so far developed, should be viewed w ithin the unified framework provided by 0t and we pursue this aim in §3. Elsewhere, improvements are made to two of the results of p a rt I. The existenceuniqueness theorem for symmetric surface waves is simplified in §2 by proving th a t exceptional transonic states are confined to the elliptical branch of the slowness section. In §4 we take up again the question of the existence of elastic surface waves consisting of a single inhomogeneous plane wave. The argum ent given in Appendix A of p a rt I is incomplete and defective inasmuch as the m atrix elements and s2 in equation (A 5)4 are zero. We obtain in §4 necessary and sufficient conditions for the existence of a one-component surface wave and deduce th a t there is no symmetric wave of this kind.
doi:10.1098/rspa.1991.0071
fatcat:fmim3mobzfd4xjwxc4s6vo2twq