 | | 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
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| In English (Mech. Solids): | | 3212 |
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| A. M. Akhtyamov, "Identification of the type of support of an annular plate by its natural vibration frequencies," Mech. Solids. 38 (6), 111-119 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
6 |
Pages |
111-119 |
| Title |
Identification of the type of support of an annular plate by its natural vibration frequencies |
| Author(s) |
A. M. Akhtyamov (Ufa) |
| Abstract |
The ability of the type of support of an annular plate along its inner and outer contours to be identified by natural frequencies of axially symmetric vibrations of the plate is justified. It is proved that the solution of the appropriate inverse problem is unique. A method for identification of the boundary conditions by a finite set of consecutive lower natural frequencies is proposed. Example problems of identification of the type of support of a plate along the inner and outer contours by three natural frequencies are considered. |
| References |
| 1. | I. E. Sakharov, "Natural vibration frequencies for annular plates," Izv. AN SSSR. OTN, No. 5, pp. 107-110, 1957. |
| 2. | V. S. Gontkevich, Natural Vibrations of Plates and Shells
[in Russian], Naukova Dumka, Kiev, 1964. |
| 3. | B. V. Pavlov, Acoustic Diagnostics of Mechanisms [in Russian], Mashinostroenie, Moscow, 1971. |
| 4. | I. A. Birger, Engineering Diagnostics [in Russian],
Mashinostroenie, Moscow, 1978. |
| 5. | M. Kac, "Can one hear the shape of a drum?" Amer. Math. Monthly, Vol. 73, No. 4, pp. 1-23, 1966. |
| 6. | A. M. Akhtyamov, "On the identification of a boundary condition by a finite set of eigenvalues," Differentsial'nye Uravneniya [Differential Equations], Vol. 35, No. 8,
pp. 1127-1128, 1999. |
| 7. | V. A. Sadovnichii, Ya. T. Sultanaev, and A. M. Akhtyamov,
"Analogues of Borg's uniqueness theorem for the case of
coupled boundary conditions," Doklady AN, Vol. 367, No. 6,
pp. 739-741, 1999. |
| 8. | A. M. Akhtyamov, "On the uniqueness of restotation of the boundary conditions of the Sturm-Liouville problem by its spectrum," Matematicheskoe Modelirovanie, Vol. 12, No. 3, p. 6, 2000. |
| 9. | A. M. Akhtyamov, "On the uniqueness of restoration of the boundary conditions of a spectral problem by its spectrum,"
Fundamental'naya i Prikladnaya Matematika, Vol. 6, No. 4,
pp. 995-1006, 2000. |
| 10. | I. Sh. Akhatov and A. M. Akhtyamov, "Identification of
the type of support of a beam by natural frequencies of its
flexural vibrations," PMM [Applied Mathematics and Mechanics],
Vol. 65, No. 2, pp. 290-298, 2001. |
| 11. | W. Strutt (Lord Rayleigh), The Theory of Sound. Volume 1,
Macmillan, London, 1929. |
| 12. | V. V. Bolotin (Editor), Vibrations in Engineering. A handbook. Volume 1:
Vibrations of Linear Systems [in Russian],
Mashinostroenie, Moscow, 1978. |
| 13. | I. A. Birger and Ya. G. Panovko (Editors), Strength, Stability,
and Vibrations. A Handbook. Volume 1 [in Russian],
Mashinostroenie, Moscow, 1968. |
| 14. | P. Lancaster, Theory of Matrices, Acad. Press, N.Y.,
London, 1969. |
| 15. | M. A. Naimark, Linear Differential Operators [in Russian], Nauka, Moscow, 1969. |
| 16. | A. F. Nikiforov and V. B. Uvarov, Special Functions of Mathematical Physics [in Russian], Nauka, Moscow, 1984. |
| 17. | E. Janke, F. Emde, and F. Löesch, Tables of Higher Functions [Russian translation], Nauka, Moscow, 1968. |
| 18. | B. Ya. Levin, Distribution of Roots of Entire Functions
[in Russian], Gostekhizdat, Moscow, 1956. |
| 19. | M. M. Postnikov, Lectures on Geometry. Linear Algebra and Differential Geometry [in Russian], Nauka, Moscow, 1979. |
| 20. | K. Rektoris, Variational Methods in Mathematics, Science, and Engineering [Russian translation], Mir, Moscow, 1985. |
|
| Received |
14 March 2002 |
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