Loading [MathJax]/jax/output/SVG/config.js
Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find




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

Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2015, Volume 55, Number 10, Pages 1713–1726
DOI: https://doi.org/10.7868/S0044466915100178 (Mi zvmmf10285) 		 
Eigenmodes of a thin elastic layer between periodic rigid profiles

S. A. Nazarovabc

a St. Petersburg State University, Universitetskii pr. 28, Peterhof, St. Petersburg, 198504, Russia
b St. Petersburg State Polytechnical University, Politekhnicheskaya ul. 29, St. Petersburg, 195251, Russia
c Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, Bolshoi pr. 61, V.O., St. Petersburg, 199178, Russia
Full-text PDF (649 kB)
References:
PDF
HTML
DOI: https://doi.org/10.7868/S0044466915100178
Abstract: Asymptotic expansions of the eigenfrequencies and eigenmodes of a thin three-dimensional elastic gasket clamped between two finite or infinite periodic rigid profiles are constructed. It is shown that the stresses are localized and concentrated near the point where the thickness of the gasket is maximal, and the character of a possible fracture is discussed. It is found that there are multiple zones of wave stopping in an elastic periodic layer and the eigenfrequencies at which elastic modes are trapped are condensed at a local perturbation of the waveguide shape.
Key words: curved elastic gasket, rigid profiles, asymptotics, eigenoscillations, concentration of stresses, periodic elastic layer, stopping zones, wave trapping.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-02175
Received: 25.02.2015
English version:
Computational Mathematics and Mathematical Physics, 2015, Volume 55, Issue 10, Pages 1684–1697
DOI: https://doi.org/10.1134/S0965542515100164
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: S. A. Nazarov, “Eigenmodes of a thin elastic layer between periodic rigid profiles”, Zh. Vychisl. Mat. Mat. Fiz., 55:10 (2015), 1713–1726; Comput. Math. Math. Phys., 55:10 (2015), 1684–1697
Citation in format AMSBIB
\Bibitem{Naz15}
\by S.~A.~Nazarov
\paper Eigenmodes of a thin elastic layer between periodic rigid profiles
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2015
\vol 55
\issue 10
\pages 1713--1726
\mathnet{http://mi.mathnet.ru/zvmmf10285}
\crossref{https://doi.org/10.7868/S0044466915100178}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3412535}
\elib{https://elibrary.ru/item.asp?id=24149961}
\transl
\jour Comput. Math. Math. Phys.
\yr 2015
\vol 55
\issue 10
\pages 1684--1697
\crossref{https://doi.org/10.1134/S0965542515100164}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000363056200009}
\elib{https://elibrary.ru/item.asp?id=24961857}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84944459645}
Linking options:
  • https://www.mathnet.ru/eng/zvmmf10285
  • https://www.mathnet.ru/eng/zvmmf/v55/i10/p1713
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Statistics & downloads:
    Abstract page:363
    Full-text PDF :81
    References:91
    First page:11
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025