 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 53, Issue 5 / 2018 | Next article >> |
| D.V. Ukrainskii, "On the Type of Flexural Edge Wave on a Circular Plate," Mech. Solids. 53 (5), 501-509 (2018) |
| Year |
2018 |
Volume |
53 |
Number |
5 |
Pages |
501-509 |
| DOI |
10.3103/S0025654418080046 |
| Title |
On the Type of Flexural Edge Wave on a Circular Plate |
| Author(s) |
D.V. Ukrainskii (Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991 Russia, d.v.ukrainskiy@gmail.com) |
| Abstract |
The article deals with the question of what is a type of flexural edge wave on a circular plate. It is shown that, in contrast to the case of a rectilinear plate, the flexural edge wave on a circular plate is a wave of a fundamentally different type, namely a whispering gallery wave. With an increase in the wave number, this wave gradually turns into an analogue of the Konenkov wave, but this happens in the region of very short waves. The dependence on Poisson's ratio (the "critical" value of the harmonic number, at which the wave transformation from whispering gallery type to the Konenkov type occurs) is constructed. The certain conditions, under which the transition region does not go beyond the scope of the Kirchhoff theory, are determined. |
| Keywords |
flexural edge wave, circular plate, whispering gallery wave, Konenkov wave |
| References |
| 1. | J.W.S. Rayleigh,
"On Waves Propagated Along the Plane Surface of an Elastic Solid,"
Proc. Lond. Math. Soc.
17 (253), 4-11 (1885). |
| 2. | R. Stoneley,
"Elastic Waves at the Surface of Separation of Two Solids,"
Proc. Roy. Soc. Lond.
106 (732), 416-428 (1924). |
| 3. | Yu.K. Konenkov,
"On a Flexural Wave of Rayleigh Type,"
Sov. Phys. Acoust.,
No. 6, 124-126 (1960). |
| 4. | V.M. Babich and V.S. Buldyrev,
Asymptotic Methods in Problems of Diffraction of Short Waves
(Nauka, Moscow, 1972) [in Russian]. |
| 5. | G.R. Kirchhoff,
"Über das Gleichgewicht und die Bewegung einer elastischen Scheibe,"
J. Reine Angew. Math.
1850 (40), 51-88 (1850). |
| 6. | M. Abramowitz and I.A. Stegun,
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
(Dover Publications, New York, 1965). |
| 7. | Yu.D. Kaplunov , E.L. Kossovich, R.R. Mukhomodyarov, and O.V. Sorokina,
"Explicit Propagation Models for Bending Edge and Interface Waves in thin Isotropic Plates,"
Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform.
13 (1), 56-63 (2013). |
|
| Received |
07 December 2017 |
| Link to Fulltext |
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