Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
in January 1966
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IssuesArchive of Issues2020-2pp.202-206

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A.M. Akhtyamov and J.A. Pardaev, "On the Identification of Common Fastenings of a Rectangular Plate," Mech. Solids. 55 (2), 202-206 (2020)
Year 2020 Volume 55 Number 2 Pages 202-206
DOI 10.3103/S002565442002003X
Title On the Identification of Common Fastenings of a Rectangular Plate
Author(s) A.M. Akhtyamov (Bashkir State University, Ufa, Russia; Mavlyutov Institute of Mechanics - Subdivision of the Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa, Russia,
J.A. Pardaev (Jizzakh State Pedagogical Institute named after A. Kadyri, Jizzakh, Uzbekistan,
Abstract A rectangular plate pivotally mounted on two opposite edges is considered. It is shown that one of the plate fastenings at the other two edges is determined up to a permutation of the fastenings at these edges uniquely from five natural frequencies. It is also shown that four eigenfrequencies for such a recovery is not enough. The corresponding counterexample is given. It was previously shown that the general boundary conditions at the two edges of a rectangular plate can be uniquely determined by 9 eigenfrequencies. The method used earlier was based on the reconstruction of the matrix accurate to linear row transformations. Such a matrix is restored up to linear transformations of strings by a vector determined up to a constant factor and made up of 10 fourth-order minors of such a matrix. The method used in this work is based on the restoration of elastic canonical boundary conditions for which it is assumed that the stiffness coefficients of elastic fastenings can be zero or infinity.
Keywords rectangular plate, boundary inverse problem, boundary conditions, eigenfrequencies
Received 04 July 2019Revised 15 July 2019Accepted 27 July 2019
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