 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| << Previous article | Volume 58, Issue 7 / 2023 | Next article >> |
| O.V. Fadeeva, "Inverse Problems for Equations of Vibrations of a Cantilever Beam for the Determination of Source," Mech. Solids. 58 (7), 2649-2655 (2023) |
| Year |
2023 |
Volume |
58 |
Number |
7 |
Pages |
2649-2655 |
| DOI |
10.3103/S0025654423070087 |
| Title |
Inverse Problems for Equations of Vibrations of a Cantilever Beam for the Determination of Source |
| Author(s) |
O.V. Fadeeva (Samara State Technical University, Samara Russia, faoks@yandex.ru) |
| Abstract |
For the beam vibration equation, inverse problems are studied, in which the right-hand
side, i.e., vibration source, is determined. Solutions of the problems using methods of spectral analysis
and the Volterra integral equations are constructed explicitly as sums of series, and the corresponding
uniqueness and existence theorems are proved. In substantiating the existence of a solution to the
inverse problem, in which the right-hand-side factor depending on a spatial coordinate is determined,
the problem of small denominators arises. In relation to this, denominator estimates are found that
guarantee their separation from zero, with an indication of the corresponding asymptotic behavior.
Based on these estimates, the convergence of the series in the class of regular solutions of the beam
vibration equation is substantiated. |
| Keywords |
beam equation, inverse problems, spectral analysis method, uniqueness, existence, Volterra integral equation |
| Received |
15 May 2023 | Revised |
15 June 2023 | Accepted |
20 June 2023 |
| Link to Fulltext |
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