 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
|
| In English (Mech. Solids): | | 3212 |
|
| << Previous article | Volume 52, Issue 3 / 2017 | Next article >> |
| V.M. Byrdin, "Normal Wave Diffraction on a Plate Submerged in a Liquid: Level Gauge Model, Factorization Method Modification, and Waveguide Quasiresonances," Mech. Solids. 52 (3), 299-314 (2017) |
| Year |
2017 |
Volume |
52 |
Number |
3 |
Pages |
299-314 |
| DOI |
10.3103/S0025654417030074 |
| Title |
Normal Wave Diffraction on a Plate Submerged in a Liquid: Level Gauge Model, Factorization Method Modification, and Waveguide Quasiresonances |
| Author(s) |
V.M. Byrdin (Blagonravov Institute of Mechanical Engineering of the Russian Academy of Sciences, Malyi Kharitonievskii per. 4, Moscow, 101990 Russia, v_m_byrdin@mail.ru) |
| Abstract |
An exact solution is obtained for one more new diffraction problem whose transcendental difficulty has been known since Sommerfeld and Kirchhoff. The model of waveguide level gauge, where the main problem is the bulk diffraction of normal waves in a layered structure consisting of an elastic plate between two semi-infinite liquid layers, is investigated. The boundary value problem is solved by using a modification of the Wiener-Hopf factorization method; the factorization is used twice to solve two systems of underdetermined functional equations, and this is a specific characteristics of the problem and a methodological novelty. The proposed modification is acceptable for the class of such problems. The diffracted spectra are analyzed; the waveguide quasiresonances are physically treated; the effect of pure Lamb wave propagation under the liquid is established; the narrow-band backward-wave modes are determined. |
| Keywords |
diffraction, layered structure, modified factorization method, underdetermined equations, normal waves, narrow-band backward waves, waveguide quasiresonance, waveguide acoustic level gauge |
| References |
| 1. | A. M. Lerer,
"On the Solution of Some Generalized Wiener-Hopf Equations,"
Radiotekhn. Elektron.
24 (2), 213-220 (1979)
[J. Commun. Technol. Electron. (Engl. Transl.)]. |
| 2. | L. A. Vainstein,
Diffraction Theory. SHF Electrodynamics,
in Collective Works,
Ed. by S. M. Rytov
(Radio i Svyaz', Moscow, 1995)
[in Russian]. |
| 3. | L. Lewin,
Theory of Waveguides: Techniques for the Solution of Waveguide Problem
(Radio i Svyaz', Moscow, 1981)
[in Russian]. |
| 4. | B. Noble,
Methods Based on the Wiener-Hopf Technique for Solving Partial Differential Equations
(Pergamon, New York, 1958; Izdat. Inostr. Lit., Moscow, 1962). |
| 5. | V. A. Fok,
"On Some Integral Equations of Mathematical Physics,"
Mat. Sb.
14 (1-2), 3-50 (1944). |
| 6. | L. A. Tkacheva,
"Action of a Periodic Load on an Elastic Floating Plate,"
Izv. Ross. Akad. Nauk. Mekh. Zhidk. Gaza.,
No. 2, 132-146 (2005)
[Fluid Dyn. (Engl. Transl.)
40 (2), 282-296 (2005)]. |
| 7. | M. Sh. Israilov,
Dynamic Theory of Elasticity and Wave Diffraction
(Izdat. MGU, Moscow, 1992)
[in Russian]. |
| 8. | L. G. Merkulov and S. I. Rokhlin,
"Lamb Wave Diffraction at a Semi-Infinite Cut in a Plate,"
Defektoskopiya,
No. 4, 35-42 (1969)
[Soviet J. Nondestruct. Testing (Engl. Transl.)]. |
| 9. | S. I. Rokhlin,
"Diffraction of Lamb's Waves by a Finite Crack in an Elastic Layer,"
J. Acoust. Soc. Amer.
67 (4), 1157-1165 (1980). |
| 10. | L. G. Merkulov and S. I. Rokhlin,
"Wave Diffraction at a Half-Infinite Plate-Liquid Contact,"
in 18th Sci. Conf. TRTI
(TRTI, Taganrog, 1972),
pp. 14-15
[in Russian]. |
| 11. | P. P. Kremlevskii,
Flowmeters and Quantity Meters: Handbook
(Leningrad, Mashinostroenie, 1989)
[in Russian]. |
| 12. | A. Erdelyi,
Asymptotic Expansions
(Dover, New York, 1956; Fizmatlit, Moscow, 1962). |
| 13. | A. G. Sveshnikov and A. N. Tikhonov,
Theory of Functions of a Complex Variable
(Fizmatlit, Moscow, 2004)
[in Russian]. |
| 14. | V. K. Astashev, V. I. Babitsky, A. M. Veprik, and V. L. Krupenin,
"Damping of Rod and String Vibrations by a Washer,"
Dokl. Akad. Nauk SSSR
304 (1), 50-54 (1989). |
| 15. | V. M. Byrdin,
"Radiation Conditions for Some Boundary-Value Problems with Helmholtz Equations,"
Dokl. Akad. Nauk SSSR
238 (2), 293-295 (1978)
[Sov. Phys. Dokl. (Engl. Transl.)]. |
| 16. | V. T. Grinchenko and V. V. Meleshko,
Harmonic Vibrations and Waves in Elastic Bodies
(Naukova Dumka, Kiev, 1981)
[in Russian]. |
| 17. | A. S. Silbergleit and Yu. I. Kopilevich,
Spectral Theory of Regular Waveguides
(Leningrad, FTI, 1983)
[in Russian]. |
| 18. | N. A. Shul'ga,
"Propagation of Harmonic Waves in Anisotropic Piezoelectric Cylinders. Compound Waveguides,"
Prikl. Mekh.
38 (12), 33-54 (2002)
[Int. Appl. Mech. (Engl. Transl.)
38 (12), 1440-1458 (2002)]. |
| 19. | L. V. Kantorovich and V. I. Krylov,
Approximate Methods of Higher Analysis
(Fizmatgiz, Moscow-Leningrad, 1962; Interscience, New York, 1964). |
| 20. | R. G. Cooke,
Infinite Matrices and Sequence Spaces
(Macmillan and Company, Ltd., London, 1950; Fizmatlit, Moscow, 1960). |
| 21. | V. M. Byrdin,
"Antispecular Reflections in the Backward-Wave Multimode Systems,"
Radiotekhn. Elektron.
57 (1), 80-86 (2012)
[J. Commun. Technol. Electron. (Engl. Transl.)
57 (1), 75-81 (2012)]. |
| 22. | R. V. Goldstein, V. A. Gorodtsov, and D. S. Lisovenko,
"Rayleigh and Love Surface Waves in Isotropic Media with Negative Poisson's Ratio,"
Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 74-89 (2014)
[Mech. Solids (Engl. Transl.)
49 (4), 422-434(2014)]. |
| 23. | V. M. Byrdin,
"Concept of Backward-Wave Antidiffraction in General Wave Theory:
Phenomena of Heteronymous Antidiffraction and Afraction in Multimode Systems,"
in Proc. XI All-Russia Meeting in Fundamental Problems of
Theoretical and Appllied Mechanics, Kazan, August 20-24. 2015
(KFU, Kazan, 2015),
pp. 656-657
[in Russian]. |
| 24. | V. M. Byrdin,
"Dispersion, Approximation, and Asymptotics of Backward, Normal, and Dispersing Waves,"
Probl. Mashinostr. Avtomatizatsii,
No. 1, 102-109 (2007). |
|
| Received |
20 January 2015 |
| Link to Fulltext |
|
| << Previous article | Volume 52, Issue 3 / 2017 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English