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Israel Ashdod
Section Mechanics
Title On the determination of loading and fixing for one end of a rod according to its natural frequencies of oscillation
Author(-s) Akhtyamov A.M.ab, Muftakhov A.V.c, Akhtyamova A.A.a
Affiliations Bashkir State Universitya, Institute of Mechanics, Ufa Centre of the Russian Academy of Sciencesb, Shamoon College of Engineeringc
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
UDC 534.113
MSC 35Q74, 74J25, 34B09
DOI 10.20537/vm130309
Received 19 February 2013
Language Russian
Citation Akhtyamov A.M., Muftakhov A.V., Akhtyamova A.A. On the determination of loading and fixing for one end of a rod according to its natural frequencies of oscillation, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 3, pp. 114-129.
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