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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, Issue 3, Pages 114–129
(Mi vuu393)
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This article is cited in 11 scientific papers (total in 11 papers)
MECHANICS
On the determination of loading and fixing for one end of a rod according to its natural frequencies of oscillation
A. M. Akhtyamovab, A. V. Muftakhovc, A. A. Akhtyamovad a Institute of Mechanics, Ufa Centre of the Russian Academy of Sciences, pr. Oktyabrya, 71, Ufa, 450054, Russia
b Department of Continuum Mechanics, Faculty of Mathematics and Information Technology, Bashkir State University, ul. Zaki Validi, 32, Ufa, 450076, Russia
c Shamoon College of Engineering, Jabotinski st., 84, Ashdod, 77245, Israel
d Department of Mathematics and Information Technology, Bashkir State University, ul. Zaki Validi, 32, Ufa, 450054, Russia
Abstract:
The identification problem of fixing conditions for a beam according to five natural frequencies of its vibrations is considered. On the basis of Plucker's conditions arising at the restoration of a matrix according to its minors of the maximal order, the set of well-posedness of the problem is constructed and the correctness according to A. N. Tikhonov is proved. We have found an explicit solution to the problem of the identification matrix of the boundary conditions, the above solution is written out in terms of the characteristic determinant for the corresponding spectral problem. The corresponding examples are provided.
Keywords:
eigenvalues, inverse problem, natural frequencies, beam, concentrated inertial element.
Received: 19.02.2013
Citation:
A. M. Akhtyamov, A. V. Muftakhov, A. A. Akhtyamova, “On the determination of loading and fixing for one end of a rod according to its natural frequencies of oscillation”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, no. 3, 114–129
Linking options:
https://www.mathnet.ru/eng/vuu393 https://www.mathnet.ru/eng/vuu/y2013/i3/p114
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