Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Surface wave running along the edge of an elastic wedge

Author: I. V. Kamotskiĭ
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 20 (2008), nomer 1.
Journal: St. Petersburg Math. J. 20 (2009), 59-63
MSC (2000): Primary 74J15
Published electronically: November 13, 2008
MathSciNet review: 2411969
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The existence of the waves mentioned in the title is proved for the case of an acute wedge.

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

  • 1. A. A. Maradudin et al., Vibrational edge modes in finite crystals, Phys. Rev. B 6 (1972), 1106-1111.
  • 2. P. E. Lagasse, Analysis of a dispersion-free guides for elastic waves, Electron. Lett. 8 (1972), no. 15, 372-373.
  • 3. V. V. Krylov, Geometro-acoustical approach to description of localized modes for vibration of a solid elastic wedge, Zh. Tekhn. Fiz. 60 (1990), no. 2, 1-7. (Russian)
  • 4. A. V. Shanin, Excitation and scattering of a wedge wave in an elastic wedge with angle close to $ 180^{\circ}$, Akust. Zh. 43 (1997), no. 3, 402-408. (Russian)
  • 5. D. V. Evans, M. Levitin, and D. Vassiliev, Existence theorems for trapped modes, J. Fluid Mech. 261 (1994), 21-31. MR 1265871 (94m:76113)
  • 6. A. S. Bonnet-Ben Dhia, J. Duterte, and P. Joly, Mathematical analysis of elastic surface waves in topographic waveguides, Math. Models Methods Appl. Sci. 9 (1999), 755-798. MR 1697393 (2000d:74036)
  • 7. I. V. Kamotskiĭ and S. A. Nazarov, Elastic waves localized near periodic families of defects, Dokl. Akad. Nauk 368 (1999), no. 6, 771-773; English transl., Dokl. Phys. 44 (1999), no. 10, 715-717. MR 1749046 (2001c:74043)
  • 8. G. Duvaut and J.-L. Lions, Les inéquations en mécanique et en physique, Travaux Rech. Math., No. 21, Dunod, Paris, 1972. MR 0464857 (57:4778)
  • 9. C. Amrouche and V. Girault, Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension, Czechoslovak Math. J. 44 (1994), 109-140. MR 1257940 (95c:35190)
  • 10. I. M. Glazman, Direct methods of qualitative spectral analysis of singular differential operators, Fizmatgiz, Moscow, 1963; English transl., Daniel Davey and Co., Inc., New York, 1966. MR 0185471 (32:2938); MR 0190800 (32:8210)
  • 11. M. Sh. Birman and M. Z. Solomyak, Spectral theory of selfadjoint operators in Hilbert space, Leningrad. Univ., Leningrad, 1980; English transl., Reidel, Dordrecht, 1987. MR 0609148 (82k:47001); MR 1192782 (93g:47001)

Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2000): 74J15

Retrieve articles in all journals with MSC (2000): 74J15

Additional Information

I. V. Kamotskiĭ

Keywords: Surface wave, Reyleigh wave, acute wedges, variational principle
Received by editor(s): April 5, 2007
Published electronically: November 13, 2008
Additional Notes: Supported by RFBR, grant no. 07-01-00548
Article copyright: © Copyright 2008 American Mathematical Society

American Mathematical Society