Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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 4 scientific papers (total in 4 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 (4)
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}
Linking options:
  • https://www.mathnet.ru/eng/vspua175
  • https://www.mathnet.ru/eng/vspua/v7/i3/p518
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
    Statistics & downloads:
    Abstract page:16
    Full-text PDF :5
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024