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Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2021, Volume 8, Issue 4, Pages 661–669
DOI: https://doi.org/10.21638/spbu01.2021.412 (Mi vspua80) 		 
MECHANICS

Plate vibrations with periodically changing parameters

N. V. Naumova, D. N. Ivanov, N. P. Dorofeev

St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
Full-text PDF (298 kB)
DOI: https://doi.org/10.21638/spbu01.2021.412
Abstract: Vibrations of square plate with periodically changing parameters are considered. The averaged fourth-order partial differential equation for the plate deflection w is offered. Solution of the problem is obtained by using the approximate theory. The approximate results are presented by analytical formulas. Asymptotic averaging (realized in Wolfram Mathematica) and Finite Elements Method (ANSYS) are used to get the values of vibrations frequencies. The comparison of numerical and asymptotic results is performed.
Keywords: plate, reinforced plate, heterogeneous plate, vibrations of plates, deformations of plates.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00208-a
This work is supported by Russian Foundation for Basic Research (grant no. 19-01-00208-a).
Received: 22.03.2021
Revised: 02.05.2021
Accepted: 17.07.2021
English version:
Vestnik St. Petersburg University, Mathematics, 2021, Volume 8, Issue 4, Pages 411–417
DOI: https://doi.org/10.1134/S1063454121040130
Document Type: Article
UDC: 539.3
MSC: 74K20, 74H45
Language: Russian
Citation: N. V. Naumova, D. N. Ivanov, N. P. Dorofeev, “Plate vibrations with periodically changing parameters”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 8:4 (2021), 661–669; Vestn. St. Petersbg. Univ., Math., 8:4 (2021), 411–417
Citation in format AMSBIB
\Bibitem{NauIvaDor21}
\by N.~V.~Naumova, D.~N.~Ivanov, N.~P.~Dorofeev
\paper Plate vibrations with periodically changing parameters
\jour Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
\yr 2021
\vol 8
\issue 4
\pages 661--669
\mathnet{http://mi.mathnet.ru/vspua80}
\crossref{https://doi.org/10.21638/spbu01.2021.412}
\transl
\jour Vestn. St. Petersbg. Univ., Math.
\yr 2021
\vol 8
\issue 4
\pages 411--417
\crossref{https://doi.org/10.1134/S1063454121040130}
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