RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Sibirsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






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


Sibirsk. Mat. Zh., 2012, Volume 53, Number 2, Pages 345–364 (Mi smj2310)  

This article is cited in 3 scientific papers (total in 3 papers)

Asymptotics of solutions to the spectral elasticity problem for a spatial body with a thin coupler

S. A. Nazarov

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg

Abstract: We construct asymptotics for the eigenvalues and vector eigenfunctions of the elasticity problem for an anisotropic body with a thin coupler (of diameter h) attached to its surface. In the spectrum we select two series of eigenvalues with stable asymptotics. The first series is formed by eigenvalues $O(h^2)$ corresponding to the transverse oscillations of the rod with rigidly fixed ends, while the second is generated by the longitudinal oscillations and twisting of the rod, as well as eigenoscillations of the body without the coupler. We check the convergence theorem for the first series and derive the error estimates for both series.

Keywords: joint of a massive rod with a thin rod, spectrum of elastic body, asymptotics for eigenvalues.

Full text: PDF file (410 kB)
References: PDF file   HTML file

English version:
Siberian Mathematical Journal, 2012, 53:2, 274–290

Bibliographic databases:

Document Type: Article
UDC: 517.956.8+517.956.328+539.3(4)
Received: 05.02.2011

Citation: S. A. Nazarov, “Asymptotics of solutions to the spectral elasticity problem for a spatial body with a thin coupler”, Sibirsk. Mat. Zh., 53:2 (2012), 345–364; Siberian Math. J., 53:2 (2012), 274–290

Citation in format AMSBIB
\Bibitem{Naz12}
\by S.~A.~Nazarov
\paper Asymptotics of solutions to the spectral elasticity problem for a~spatial body with a~thin coupler
\jour Sibirsk. Mat. Zh.
\yr 2012
\vol 53
\issue 2
\pages 345--364
\mathnet{http://mi.mathnet.ru/smj2310}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2975940}
\transl
\jour Siberian Math. J.
\yr 2012
\vol 53
\issue 2
\pages 274--290
\crossref{https://doi.org/10.1134/S0037446612020103}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000303357900010}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84860371544}


Linking options:
  • http://mi.mathnet.ru/eng/smj2310
  • http://mi.mathnet.ru/eng/smj/v53/i2/p345

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Bunoiu R., Cardone G., Nazarov S.A., “Scalar Boundary Value Problems on Junctions of Thin Rods and Plates”, ESAIM-Math. Model. Numer. Anal.-Model. Math. Anal. Numer., 48:5 (2014), 1495–1528  crossref  mathscinet  zmath  isi  scopus
    2. F. L. Bakharev, S. A. Nazarov, “Gaps in the spectrum of a waveguide composed of domains with different limiting dimensions”, Siberian Math. J., 56:4 (2015), 575–592  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. Yu. I. Dimitrienko, I. D. Dimitrienko, “Modeling of thin composite laminates with general anisotropy under harmonic vibrations by the asymptotic homogenization method”, Int. J. Multiscale Comput. Eng., 15:3 (2017), 219–237  crossref  isi  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
    Number of views:
    This page:205
    Full text:43
    References:39
    First page:14

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019