|
Surface wave running along the edge of an elastic wedge
Author(s):
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
Posted:
November 13, 2008
MathSciNet review:
2411969
Retrieve article in:
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:
-
- 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
, 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
Email:
i.kamotski@maths.bath.ac.uk
DOI:
10.1090/S1061-0022-08-01037-6
PII:
S 1061-0022(08)01037-6
Keywords:
Surface wave,
Reyleigh wave,
acute wedges,
variational principle
Received by editor(s):
5/APR/2007
Posted:
November 13, 2008
Additional Notes:
Supported by RFBR, grant no. 07-01-00548
Copyright of article:
Copyright
2008,
American Mathematical Society
|