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Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, Volume 7, Issue 3, Pages 518–526
DOI: https://doi.org/10.21638/spbu01.2020.314 (Mi vspua175) 		 
This article is cited in 5 scientific papers (total in 5 papers)

MECHANICS

Free vibration frequencies of a circular thin plate with variable parameters

G. P. Vasiliev, A. L. Smirnov

St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
Full-text PDF (1351 kB) Citations (5)
DOI: https://doi.org/10.21638/spbu01.2020.314
Abstract: Transverse vibrations of an inhomogeneous circular thin plate are studied in the paper. Nondimensional equations based on Kirchhoff - Love hypotheses describing nonaxisymmetric vibrations of inhomogeneous plate are derived. Using the perturbation method, asymptotic formulas are obtained for the free vibration frequencies of a plate, whose thickness and Young's modulus linearly depend on the radial coordinate. The influence of the plate edge conditions on the frequencies and the behavior of frequencies for a plate with the fixed mass are analyzed. For the lower free vibration frequencies the results of asymptotic and finite elements analyses are compared.
Keywords: free vibrations of plates, inhomogeneous circular plate, perturbation method.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00832-a
19-01-00208-a
The work is supported by Russian Foundation for Basic Research (grant no. 18-01-00832-a and 19-01-00208-a).
Received: 21.02.2020
Revised: 18.03.2020
Accepted: 19.03.2020
English version:
Vestnik St. Petersburg University, Mathematics, 2020, Volume 7, Issue 3, Pages 351–357
DOI: https://doi.org/10.1134/S1063454120030140
Document Type: Article
UDC: 534.1:539.3
MSC: 73K12
Language: Russian
Citation: G. P. Vasiliev, A. L. Smirnov, “Free vibration frequencies of a circular thin plate with variable parameters”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 7:3 (2020), 518–526; Vestn. St. Petersbg. Univ., Math., 7:3 (2020), 351–357
Citation in format AMSBIB
\Bibitem{VasSmi20}
\by G.~P.~Vasiliev, A.~L.~Smirnov
\paper Free vibration frequencies of a circular thin plate with variable parameters
\jour Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
\yr 2020
\vol 7
\issue 3
\pages 518--526
\mathnet{http://mi.mathnet.ru/vspua175}
\crossref{https://doi.org/10.21638/spbu01.2020.314}
\transl
\jour Vestn. St. Petersbg. Univ., Math.
\yr 2020
\vol 7
\issue 3
\pages 351--357
\crossref{https://doi.org/10.1134/S1063454120030140}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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