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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, Issue 3, Pages 114–129 (Mi vuu393)  

This article is cited in 6 scientific papers (total in 6 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.

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Document Type: Article
UDC: 534.113
MSC: 35Q74, 74J25, 34B09
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

Citation in format AMSBIB
\Bibitem{AkhMouAkh13}
\by A.~M.~Akhtyamov, A.~V.~Muftakhov, A.~A.~Akhtyamova
\paper On the determination of loading and fixing for one end of a~rod according to its natural frequencies of oscillation
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2013
\issue 3
\pages 114--129
\mathnet{http://mi.mathnet.ru/vuu393}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Sadovnichii V.A., Sultanaev Ya.T., Akhtyamov A.M., “a Generalization of Levinson'S Uniqueness Theorem To the Case of General Boundary Conditions”, Dokl. Math., 90:3 (2014), 715–718  crossref  mathscinet  zmath  isi  elib  scopus
    2. Sadovnichii V.A., Sultanaev Ya.T., Akhtyamov A.M., “a Generalization of Borg'S Uniqueness Theorems For a Symmetric Potential To General Boundary Conditions”, Dokl. Math., 90:2 (2014), 565–568  crossref  mathscinet  zmath  isi  elib  scopus
    3. Akhtyamov A.M., Utyashev I.M., “Identification of Boundary Conditions At Both Ends of a String From the Natural Vibration Frequencies”, Acoust. Phys., 61:6 (2015), 615–622  crossref  mathscinet  isi  elib  scopus
    4. Akhymbek M.E., Yessirkegenov N.A., Sadybekov M.A., “Renovation of the Fixing and Loading Factors of the Beam By the Spectral Data of Free Flexural Vibrations”, AIP Conference Proceedings, 1676, eds. Ashyralyev A., Malkowsky E., Lukashov A., Basar F., Amer Inst Physics, 2015, 020058  crossref  isi  scopus
    5. A. O. Vatulyan, L. V. Vasilev, “Ob opredelenii parametrov zakrepleniya neodnorodnoi balki pri nalichii zatukhaniya”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 16:4 (2016), 449–456  mathnet  crossref  mathscinet  elib
    6. A. A. Aitbaeva, A. M. Akhtyamov, “Identification of the fixedness and loadedness of an end of an Euler–Bernoulli beam from its natural vibration frequencies”, J. Appl. Industr. Math., 11:1 (2017), 1–7  mathnet  crossref  crossref  mathscinet  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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