A short review is presented of progress in the theory of localized eigenwaves in anisotropic solids. The main attention is paid to the problem of existence of surface wave solutions in semi-infinite elastic bodies. Here the contribution of David Barnett is most important. The general theorems of existence and uniqueness are formulated and their modifications for media with piezoelectric and/or piezomagnetic couplings are considered. The conditions for existence of supersonic surface waves in purely elastic half-spaces are displayed. The situations on both sides of the vicinity of exceptional transonic states are discussed. The criterion for the existence of quasi-bulk subsonic surface waves in elastic media of unrestricted anisotropy is obtained in terms of the general Barnett and Lothe theorem. The conditions for the existence of exceptional bulk waves and their main properties are considered. The interface wave theory of David Barnett et al is reviewed for rigid and slip contacts between elastic and piezoelectric sub-media.
Stroh, A.N.Steady state problems in anisotropic elasticity . Journal of Mathematical Physics, 41, 77-103 (1962).
2.
Ingebrigtsen, K.A. and Tonning, A.Elastic surface waves in crystals. Physical Review, 184, 942-951 (1969).
3.
Barnett, D.M. and Lothe, J.Consideration of the existence of surface wave (Rayleigh wave) solutions in anisotropic elastic crystals. Journal of Physics F: Metal Physics, 4, 671-676 (1974).
4.
Lothe, J. and Barnett, D.M.On the existence of surface wave solutions for anisotropic half-spaces with free surface. Journal of Applied Physics, 47, 428-433 (1976).
5.
Chadwick, P. and Smith, G.D.Foundations of the theory of surface waves in anisotropic elastic materials , in Advances in Applied Mechanics, pp. 303-376, ed. C.-S. Yih, Academic, New York, 1977.
6.
Lyubimov, V.N. and Sannikov, D.G.Surface quasi-bulk and Rayleigh elastic waves in crystals. Soviet Physics-Solid State, 15, 830-831 (1973).
7.
Lyubimov, V.N. and Sannikov, D.G.Surface quasi-bulk waves in the neighborhood of exceptional directions and surfaces in crystals. Soviet Physics-Solid State, 17, 300-302 (1975).
8.
Lothe, J. and Alshits, V.I.Existence criterion for quasi-bulk surface waves. Soviet Physics-Crystallography , 22, 519-525 (1977).
9.
Alshits, V.I. and Lothe, J.Surface waves in hexagonal crystals. Soviet Physics-Crystallography, 23, 509-515 (1978).
10.
Chadwick, P. and Smith, G.D.Surface waves in cubic elastic media, in Mechanics of Solids , pp. 47-100, ed. H. G. Hopkins and M. J. Sewel, Pergamon, Oxford, 1982.
11.
Barnett, D.M. and Lothe, J.Free surface (Rayleigh) waves in anisotropic elastic half-spaces. Proceedings of the Royal Society of London A, 402, 135-152 (1985).
12.
Chadwick, P.A general analysis of transonic states in an anisotropic elastic body. Proceedings of the Royal Society of London A, 401, 203-223 (1985).
13.
Barnett D.M. and Chadwick, P.The existence of one-component surface waves and exceptional subsequent transonic states of types 2, 4, and E1 in anisotropic elastic media, in Modern Theory of Anisotropic Elasticity and Applications, pp. 199-214, ed. J. J. Wu, T. C. T. Ting and D. M. Barnett, SIAM Proceedings Series, SIAM, Philadelphia, 1991.
14.
Barnett, D.M., Chadwick, P. and Lothe, J.The behavior of elastic surface waves polarized in a plane of material symmetry. I. Addendum. Proceedings of the Royal Society of London A, 433, 699-710 (1991).
15.
Lothe, J. and Barnett, D.M.The present status of existence considerations for acoustic surface waves in anisotropic media, in Proceedings of the International Symposium "Surface Waves in Solids and Layered Structures ISSWAS", Novosibirsk, USSR, vol. 1, pp. 116-131, 1986.
16.
Taziev, R.M.Dispersion relation for acoustic waves in an anisotropic elastic half-space. Soviet Physics-Acoustics, 35, 535-538 (1989).
17.
Barnett, D.M.Bulk, surface, and interfacial waves in anisotropic linear elastic solids. International Journal of Solids and Structures, 37, 45-54 (2000).
18.
Barnett, D.M., Lothe, J., Nishioka, K. and Asaro, R.J.Elastic surface waves in anisotropic crystals: a simplified method for calculating Rayleigh velocities using dislocation theory. Journal of Physics F: Metal Physics, 3, 1083- 1096 (1973).
19.
Chadwick, P.Wave propagation in transversely isotropic elastic media. I. Homogeneous plane waves, II. Surface waves. Proceedings of the Royal Society of London A, 422, 23-66, 67-101 (1989).
20.
Alshits, V.I., Gorkunova, A.S. and Shuvalov, A.L.Parameters of surface and bulk transonic acoustic waves in hexagonal crystals for the γ -geometry. Crystallography Reports, 39, 879-886 (1994).
21.
Barnett, D.M.On the non-existence of subsonic boundary-polarized two-component free surface waves. Physica Scripta, T44, 98-103 (1992).
22.
Barnett, D.M. and Lothe, J.Dislocations and line charges in anisotropic piezoelectric insulators. Physica Status Solidi (b), 67, 105-111 (1975).
23.
Lothe, J. and Barnett, D.M.Integral formalism for surface waves in piezoelectric crystals. Existence considerations. Journal of Applied Physics, 47, 1799-1807 (1976 ).
24.
Lothe, J. and Barnett, D.M.Further development of the theory for surface waves in piezoelectric crystals. Physica Norvegica, 8, 239-254 (1977).
25.
Bleustein, L.A new surface wave in piezoelectric materials . Applied Physics Letters, 13, 412-413 (1968).
Alshits, V.I., Darinskii, A.N. and Lothe, J.On the existence of surface waves in half-infinite anisotropic elastic media with piezoelectric and piezomagnetic properties . Wave Motion, 16, 265-283 (1992).
28.
Alshits, V.I., Darinskii, A.N., Lothe, J. and Lyubimov, V.N.Surface acoustic waves in piezocrystals: an example of surface wave existence with clamped boundary. Wave Motion, 19, 113-123 (1994).
29.
Alshits, V.I. and Lothe, J.Comments on the relation between surface wave theory and the theory of reflection. Wave Motion, 3, 297-310 (1981).
30.
Lothe, J. and Wang, L.Self-orthogonal sextic formalism for anisotropic elastic media: spaces of simple reflection and two component surface waves , Wave Motion, 21, 163-181 (1995).
31.
Wang, L. and Lothe, J.Self-orthogonal sextic formalism for simple reflection and mode conversion at the free surface of an anisotropic elastic half space. Proceedings of the Royal Society of London A, 453, 897-911 (1997).
32.
Chadwick, P.The behavior of elastic surface waves polarized in a plane of material symmetry. I. General analysis. Proceedings of the Royal Society of London A, 430, 231-240 (1990).
33.
Barnett, D.M. , Chadwick, P. and Lothe, J.The behavior of elastic surface waves polarized in a plane of material symmetry. I. Addendum. Proceedings of the Royal Society of London A, 433, 699-710 (1991).
34.
Gundersen, S.A. , Wang, L. and Lothe, J.Secluded supersonic elastic surface waves . Wave Motion, 14, 129-143 (1991).
35.
Lothe, J.Body waves in anisotropic elastic media, in Modern Theory of Anisotropic Elasticity and Applications, pp. 173-185, ed. J. J. Wu, T. C. T. Ting and D. M. Barnett, SIAM, Philadelphia, 1991.
36.
Wang, L. and Lothe, J.Simple reflection in anisotropic elastic media and its relation to exceptional waves and supersonic surface waves. Wave Motion, 16, 89-112 (1992).
37.
Darinskii, A.N. , Alshits, V.I., Lothe, J., Lyubimov, V.N. and Shuvalov, A.L.A criterion for the existence of two-component surface waves in elastically anisotropic media. Wave Motion , 28, 241-257 (1998).
38.
Aleksandrov, V.V., Velichkina, T.S., Mozhaev, V.G., Potapova, Ju. B., Khmelev, A.K. and Yakovlev, I.A.New data concerning surface Mandelstamm-Brillouin light scattering from the basal plane of germanium crystal. Physics Letters A, 162, 418-422 (1992).
39.
Norris A.N. One-component surface waves in materials with symmetry. Journal of Mechanics and Physics of Solids , 40, 1569-1582 (1992).
40.
Chadwick, P.Some remarks on the existence of one-component surface waves in elastic materials with symmetry. Physica Scripta, 44, 94-97 (1992).
41.
Wang, L. and Gundersen, S.A.Existence of one-component surface waves in anisotropic elastic media. Physica Scripta, 47, 394-404 (1993).
42.
Kosevich, Yu. A. and Syrkin, E.S.Existence criterion and properties of deeply penetrating Rayleigh waves in crystals. Soviet Physics JETP , 62, 1282 (1985).
43.
Alshits, V.I. and Lothe, J.Elastic waves in triclinic crystals. III. Existence problem and some general properties of exceptional surface waves . Soviet Physics-Crystallography, 24, 644-648 (1979).
44.
Naumenko, N.F., Bondarenko, V.S. and Perelomova , N.V.Features of volume and surface acoustic wave propagation in paratellurite crystals. Soviet Physics-Solid State, 25, 1512-1513 (1983 ).
45.
Darinskii, A.N.Quasi-bulk Rayleigh waves in semi-infinite media of arbitrary anisotropy.Wave Motion, 27, 79-93 (1998).
46.
Alshits, V.I., Deschamps, M. and Maugin, G.A.Elastic waves in anisotropic plates: short-wavelength asymptotics of the dispersion branches vn(k). Wave Motion , 37, 273-292 (2003).
47.
Lothe, J. and Wang, L.Properties of Type 6 transonic states with respect to grazing incidence reflection of bulk waves at planar free or clamped surfaces of half-infinite elastically anisotropic media. Wave Motion, 20, 41-56 (1994).
48.
Barnett, D.M., Lothe, J., Gavazza, S.D. and Musgrave, M.J.P.Considerations of the existence of interfacial (Stoneley) waves in bonded anisotropic half-spaces. Proceedings of the Royal Society of London A, 402, 153-166 (1985).
49.
Alshits, V.I. and Maugin, G.M.Dynamics of multilayers: elastic waves in an anisotropic graded or stratified plate. Wave Motion, 41, 357-394 (2005).
50.
Barnett, D.M., Gavazza, S.D. and Lothe, J.Slip waves along the interface between two anisotropic elastic half-spaces in sliding contact. Proceedings of the Royal Society of London A, 415, 389-419 (1988).
51.
Wang, L. and Lothe, J.Existence of second slip-waves in anisotropic elastic media. Wave Motion, 18, 79-99 (1993).
52.
Abudi, M. and Barnett, D.M.On the existence of interfacial (Stoneley) waves in bonded piezoelectric half-spaces. Proceedings of the Royal Society of London A, 429, 587-611 (1990).
53.
Alshits, V.I., Barnett, D.M., Darinskii, A.N. and Lothe, J.On the existence problem for localized acoustic waves on the interface between two piezocrystals. Wave Motion , 20, 233-244 (1994).
