Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



``Forbidden'' planes for Rayleigh waves

Author: Sergey V. Kuznetsov
Journal: Quart. Appl. Math. 60 (2002), 87-97
MSC: Primary 74J15; Secondary 74E10
DOI: https://doi.org/10.1090/qam/1878260
MathSciNet review: MR1878260
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Existence of ``forbidden'' planes, on which Rayleigh waves cannot propagate, is discussed. A mathematical model for anisotropic materials possessing ``forbidden'' planes is constructed. An example of transversely isotropic material having ``forbidden'' planes is presented.

References [Enhancements On Off] (What's this?)

  • [1] J. W. Strutt (Lord Rayleigh), On wave propagating along the plane surface of an elastic solid, Proc. London Math. Soc. 17, 4-11 (1885)
  • [2] R. Stoneley, The propagation of surface elastic waves in a cubic crystal, Proc. Roy. Soc. A232, 447-458 (1955) MR 0073418
  • [3] E. Dieulesaint and D. Royer, Elastic Waves in Solids, John Wiley and Sons, New York, 1980
  • [4] D. Royer and E. Dieulesaint, Rayleigh wave velocity and displacement in orthorhombic, tetragonal, and cubic crystals, J. Acoust. Soc. America 76, 1438-1444 (1985)
  • [5] T. C. Lim and G. W. Farnell, Search for forbidden directions of elastic surface-wave propagation in anisotropic crystals, J. Appl. Phys. 39, 4319-4325 (1968)
  • [6] T. C. Lim and G. W. Farnell, Character of pseudo surface waves on anisotropic crystals, J. Acoust. Soc. America 45, 845-851 (1969)
  • [7] G. W. Farnell, Properties of elastic surface waves, Phys. Acoust. 6, 109-166 (1970)
  • [8] D. M. Barnett and J. Lothe, Synthesis of the sextic and the integral formalism for dislocations, Greens functions, and surface waves in anisotropic elastic solids, Phys. Norv. 7, 13-19 (1973)
  • [9] D. M. Barnett and J. Lothe, Consideration of the existence of surface wave (Rayleigh wave) solutions in anisotropic elastic crystals, J. Phys., F: Metal Phys. 4, 671-686 (1974)
  • [10] J. Lothe and D. M. Barnett, On the existence of surface wave solutions for anisotropic elastic half-spaces with free surface, J. Appl. Phys. 47, 428 433 (1976)
  • [11] P. Chadwick and G. D. Smith, Foundations of the theory of surface waves in anisotropic elastic materials, In: Advances in Applied Mechanics 17, Academic Press, New York, 1977, pp. 303-376
  • [12] P. Chadwick and T. C. T. Ting, On the structure and invariance of the Barnett-Lothe tensors, Quart. Appl. Math. 45, 419-427 (1987) MR 910450
  • [13] S. A. Gunderson, D. M. Barnett, and J. Lothe, Rayleigh wave existence theory: A supplementary remark, Wave Motion 9, 319-321 (1987) MR 896032
  • [14] P. Chadwick, Some remarks on the existence of one-component surface waves in elastic materials with symmetry, Physica Scripta 44, 94-97 (1992)
  • [15] P. Chadwick, The application of the Stroh formalism to prestressed elastic media, Mathematics and Mechanics of Solids 2, 379-403 (1997) MR 1480856
  • [16] A. N. Stroh, Steady state problems in anisotropic elasticity, J. Math. Phys. 41, 77-103 (1962) MR 0139306
  • [17] G. T. Mase, Rayleigh wave speeds in transversely isotropic materials, J. Acoust. Soc. America 81, 1441-1446 (1987)
  • [18] G. T. Mase and G. C. Johnson, An acoustic theory for surface waves in anisotropic media, J. Appl. Mech. 54, 127-135 (1987)
  • [19] M. E. Gurtin, The Linear Theory of Elasticity. In: Handbuch der Physik, VIa/2, Springer-Verlag, 1973, pp. 1-295
  • [20] P. Hartman, Ordinary Differential Equations, John Wiley and Sons, New York, 1964 MR 0171038

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 74J15, 74E10

Retrieve articles in all journals with MSC: 74J15, 74E10

Additional Information

DOI: https://doi.org/10.1090/qam/1878260
Article copyright: © Copyright 2002 American Mathematical Society

American Mathematical Society