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Some basic properties of bulk elastic waves in anisotropic media. (English) Zbl 1163.74307

Summary: A short survey of some basic results in the theory of bulk elastic waves in anisotropic media is presented. A series of general properties of phase speed branches is deduced. Main features of the theory of acoustic axes are briefly discussed. Bulk wave modes in a semi-infinite medium with a free surface are considered: exceptional waves, the reflection problem and limiting inhomogeneous wave superposition are described.

MSC:

74-XX Mechanics of deformable solids
76-XX Fluid mechanics
Full Text: DOI

References:

[1] M.J.P. Musgrave, Crystal Acoustics, Holden-Day, San Francisco, CA, 1970.; M.J.P. Musgrave, Crystal Acoustics, Holden-Day, San Francisco, CA, 1970. · Zbl 0201.27601
[2] Musgrave, M. J.P., On the elastodynamic classification of orthorhombic media, Proc. Roy. Soc. Lond. A, 374, 401-429 (1981) · Zbl 0482.73009
[3] R.G. Payton, Elastic Wave Propagation in Transversely Isotropic Media, Martinus Nijhoff, The Hague, 1983.; R.G. Payton, Elastic Wave Propagation in Transversely Isotropic Media, Martinus Nijhoff, The Hague, 1983. · Zbl 0574.73023
[4] P. Chadwick, G.D. Smith, Surface waves in cubic elastic media, in: H.G. Hopkins, M.J. Sewel (Eds.), Mechanics of Solids, Pergamon Press, Oxford, 1982, pp. 47-100.; P. Chadwick, G.D. Smith, Surface waves in cubic elastic media, in: H.G. Hopkins, M.J. Sewel (Eds.), Mechanics of Solids, Pergamon Press, Oxford, 1982, pp. 47-100. · Zbl 0477.73017
[5] P. Chadwick, Wave propagation in transversely isotropic elastic media. I. Homogeneous plane waves II. Surface waves, Proc. Roy. Soc. Lond. A 422 (1989) 23-66, 67-101.; P. Chadwick, Wave propagation in transversely isotropic elastic media. I. Homogeneous plane waves II. Surface waves, Proc. Roy. Soc. Lond. A 422 (1989) 23-66, 67-101. · Zbl 0686.73019
[6] Alshits, V. I.; Chadwick, P., Concavities on the zonal slowness section of a transversely isotropic elastic material, Wave Motion, 25, 347-359 (1997) · Zbl 0953.74557
[7] F.I. Fedorov, Theory of Elastic Waves in Crystals, Plenum Press, New York, 1968.; F.I. Fedorov, Theory of Elastic Waves in Crystals, Plenum Press, New York, 1968.
[8] Fitzgerald, E. R.; Wright, T. W., Invariance of sound velocity sums in crystals, Phys. Stat. Sol., 24, 1, 37-44 (1967)
[9] Hayes, M., A universal connection for waves in anisotropic media, Arch. Ration. Mech. Anal., 46, 105-113 (1972) · Zbl 0294.73030
[10] Alshits, V. I.; Lothe, J., Elastic waves in triclinic crystals. II. Topology of polarization fields and some general theorems, Sov. Phys. Crystallogr., 24, 4, 393-398 (1979)
[11] Khatkevich, A. G., The acoustic axes in crystals, Sov. Phys. Crystallogr., 7, 5, 601-604 (1962) · Zbl 0127.23306
[12] Holm, P., Generic elastic media, Phys. Scr. T, 44, 122-127 (1992)
[13] Darinskii, B. M., Acoustic axes in crystals, Crystallogr. Rep., 39, 5, 697-703 (1994)
[14] Ohmachi, Y.; Uchida, N.; Niizeki, N., Acoustic wave propagation in \(TeO_2\) single crystal, J. Acoust. Soc. Am., 51, 164-168 (1972)
[15] Ledbetter, H. M.; Kriz, R. D., Elastic-wave surfaces in solids, Phys. Stat. Sol. (b), 114, 475-480 (1982)
[16] Boulanger, Ph.; Hayes, M., Acoustic axes for elastic waves in crystals: theory and applications, Proc. Roy. Soc. Lond. A, 454, 2323-2346 (1998) · Zbl 0921.73099
[17] Khatkevich, A. G., Special directions for elastic waves in crystals, Sov. Phys. Crystallogr., 9, 5, 579-582 (1964)
[18] Khatkevich, A. G., Classification of crystals by acoustic properties, Sov. Phys. Crystallogr., 22, 6, 701-705 (1977)
[19] Khatkevich, A. G., Internal conical refraction of elastic waves, Sov. Phys. Crystallogr., 7, 5, 742-745 (1962)
[20] Alshits, V. I.; Lothe, J., Elastic waves in triclinic crystals. I. General theory and the degeneracy problem, Sov. Phys. Crystallogr., 24, 4, 387-392 (1979)
[21] Herring, C., Accidental degeneracy in the energy bands of crystals, Phys. Rev., 52, 365-373 (1937)
[22] Herring, C., Role of low-energy phonons in thermal conduction, Phys. Rev., 95, 954-965 (1954) · Zbl 0058.23706
[23] Alshits, V. I.; Lothe, J., Elastic waves in triclinic crystals. III. Existence problem and some general properties of exceptional surface waves, Sov. Phys. Crystallogr., 24, 6, 644-648 (1979)
[24] Alshits, V. I.; Shuvalov, A. L., Polarization fields of elastic waves near the acoustic axes, Sov. Phys. Crystallogr., 29, 373-378 (1984)
[25] Alshits, V. I.; Shuvalov, A. L., On the effect of external influences on the bulk elastic wave properties near acoustic axes, Ferroelectr. Lett., 1, 151-154 (1984)
[26] Alshits, V. I.; Sarychev, A. V.; Shuvalov, A. L., Classification of degeneracies and analysis of their stability in the theory of elastic waves in crystals, Sov. Phys. JETP, 62, 531-539 (1985)
[27] Shuvalov, A. L., Topological features of the polarization fields of plane acoustic waves in anisotropic media, Proc. Roy. Soc. Lond. A, 454, 2911-2947 (1998) · Zbl 0927.74038
[28] An, C. X.; Hauret, G.; Chapelle, J. P., Brillouin scattering in \(Hg_2 Cl_2\), Solid State Commun., 24, 443-445 (1977)
[29] Lushnikov, S. G.; Prohorova, S. D.; Sinii, I. G.; Smolenskii, G. A., Elastic properties of the cesium deuterium selenite crystal in the monoclinic phase, Sov. Phys. Solid State, 29, 280-284 (1987)
[30] Alshits, V. I.; Lyubimov, V. N.; Sarychev, A. V.; Shuvalov, A. L., Topological characteristics of singular points of the electric field accompanying sound propagation in piezoelectrics, Sov. Phys. JETP, 66, 2, 408-413 (1987)
[31] Alshits, V. I.; Shuvalov, A. L., On acoustic axes in piezoelectric crystals, Sov. Phys. Crystallogr., 33, 1, 1-4 (1988)
[32] Every, A. G.; McCurdy, A. K., Phonon focusing in piezoelectric crystals, Phys. Rev. B, 36, 1432-1447 (1987)
[33] V.I. Alshits, V.N. Lyubimov, Elastic waves in absorptive anisotropic media: peculiarities of wave surfaces and singularities in the polarization fields, in: A. Radowicz (Ed.), Proceedings of II Workshop on Dissipation in Physical Systems, Politechnika Swietokrziska, Kielce, Poland, 1998, pp. 15-44.; V.I. Alshits, V.N. Lyubimov, Elastic waves in absorptive anisotropic media: peculiarities of wave surfaces and singularities in the polarization fields, in: A. Radowicz (Ed.), Proceedings of II Workshop on Dissipation in Physical Systems, Politechnika Swietokrziska, Kielce, Poland, 1998, pp. 15-44.
[34] Klerk, J.; Musgrave, M., Internal conical refraction of transverse elastic waves in a cubic crystal, Proc. Phys. Soc., 68, 2, 81-88 (1955)
[35] Henneke, E. G.; Green, R. E., Light-wave/elastic wave analogies in crystals, J. Acoust. Soc. Am., 45, 6, 1367-1373 (1969)
[36] Alshits, V. I.; Darinskii, A. N.; Shuvalov, A. L., Disclinations in a vector field of polarizations in acoustic and optical beams under conical refraction conditions, Sov. Phys. JETP, 69, 6, 1105-1108 (1989)
[37] Stroh, A. N., Steady state problems in anisotropic elasticity, J. Math. Phys., 41, 77-103 (1962) · Zbl 0112.16804
[38] Barnett, D. M.; Lothe, J., Consideration of the existence of surface wave (Rayleigh wave) solutions in anisotropic elastic crystals, J. Phys. F Met. Phys., 4, 671-676 (1974)
[39] Lothe, J.; Barnett, D. M., On the existence of surface wave solutions for anisotropic half-spaces with free surface, J. Appl. Phys., 47, 428-433 (1976)
[40] Barnett, D. M.; Lothe, J., Free surface (Rayleigh) waves in anisotropic elastic half-spaces, Proc. Roy. Soc. Lond. A, 402, 135-152 (1985) · Zbl 0587.73030
[41] G.D. Smith, Surface waves in cubic elastic media, Thesis, Univ. East Anglia, Norwich, UK, 1978.; G.D. Smith, Surface waves in cubic elastic media, Thesis, Univ. East Anglia, Norwich, UK, 1978.
[42] Naumenko, N. F.; Bondarenko, V. S.; Perelomova, N. V., Features of volume and surface acoustic wave propagation in paratellurite crystals, Sov. Phys. Solid State, 25, 9, 1512-1513 (1983)
[43] Alshits, V. I.; Lyubimov, V. N.; Naumenko, N. F.; Perelomova, N. V.; Shuvalov, A. L., Exceptional elastic body waves in crystals of various symmetries, Sov. Phys. Crystallogr., 30, 2, 123-126 (1985)
[44] Chadwick, P., The behavior of elastic surface waves polarized in a plane of material symmetry. 1. General analysis, Proc. Roy. Soc. Lond. A, 430, 213-240 (1990) · Zbl 0712.73016
[45] Alshits, V. I.; Lyubimov, V. N.; Shuvalov, A. L., Exceptional body waves in the neighborhoods of acoustic axes of various types, Sov. Phys. Crystallogr., 32, 4, 487-491 (1987)
[46] Alshits, V. I.; Lothe, J., Comments on the relation between surface wave theory and the theory of reflection, Wave Motion, 3, 297-310 (1981) · Zbl 0471.73018
[47] Alshits, V. I.; Darinskii, A. N.; Shuvalov, A. L., Theory of reflection of acoustoelectric waves in a semiinfinite piezoelectric medium. I. Metallized surface, Sov. Phys. Crystallogr., 34, 6, 808-812 (1989)
[48] Alshits, V. I.; Darinskii, A. N.; Shuvalov, A. L., Theory of reflection of acoustoelectric waves in a semiinfinite piezoelectric medium. II. Non-metallized surface, Sov. Phys. Crystallogr., 35, 1, 1-6 (1990)
[49] Alshits, V. I.; Darinskii, A. N.; Shuvalov, A. L., Theory of reflection of acoustoelectric waves in a semiinfinite piezoelectric medium. III. Resonance reflection in the vicinity of the leaky wave branch, Sov. Phys. Crystallogr., 36, 2, 145-152 (1991)
[50] Alshits, V. I.; Darinskii, A. N.; Shuvalov, A. L., Acoustoelectric waves in bicrystal media in conditions of a rigid contact or a vacuum gap at an interface, Crystallogr. Rep., 38, 2, 147-158 (1993)
[51] Alshits, V. I.; Darinskii, A. N.; Shuvalov, A. L., Elastic waves in infinite and semi-infinite anisotropic media, Phys. Scripta, T44, 85-93 (1992)
[52] Shuvalov, A. L.; Lothe, J., The Stroh formalism and the reciprocity properties of reflection-transmission problems in crystal piezo-acoustics, Wave Motion, 25, 331-345 (1997) · Zbl 0920.73047
[53] Lyubimov, V. N.; Alshits, V. I., Brewster reflections of elastic waves in hexagonal crystals, Sov. Phys. Crystallogr., 27, 5, 512-516 (1982)
[54] Achenbach, J. D.; Gautesen, A. K., Elastic surface waves guided by the edge of a slit, J. Sound Vibr., 53, 3, 407-416 (1977) · Zbl 0366.73020
[55] Alshits, V. I.; Deschamps, M.; Maugin, G. A., Elastic waves in anisotropic plates: short-wavelength asymptotics of the dispersion branches \(v_{\textbf{n}}(k)\), Wave Motion, 37, 3, 273-292 (2003) · Zbl 1163.74306
[56] Alshits, V. I.; Lothe, J.; Lyubimov, V. N., Surface and exceptional body elastic waves in a plate of a hexagonal crystal, Sov. Phys. Crystallogr., 28, 4, 374-378 (1983)
[57] Filippov, V. V., On exceptional bulk waves in piezoelectric crystals, Doklady Akad. Nauk BSSR, 28, 5, 412-414 (1984)
[58] Alshits, V. I.; Lyubimov, V. N., Two types of exceptional body waves in piezoelectrics and the sectors of existence of Bleustein-Gulyaev waves, Sov. Phys. Crystallogr., 30, 3, 252-256 (1985)
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