RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Izv. RAN. Ser. Mat.: Year: Volume: Issue: Page: Find

 Izv. RAN. Ser. Mat., 2013, Volume 77, Issue 1, Pages 91–144 (Mi izv7804)

Asymptotics of eigen-oscillations of a massive elastic body with a thin baffle

S. A. Nazarovab

a Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St.-Petersburg
b Saint-Petersburg State University

Abstract: We construct asymptotics of eigenvalues and eigenvectors in the elasticity problem for an anisotropic body joined to a thin plate-baffle (of variable thickness $O(h)$, $h\ll 1$). The spectrum contains two series of eigenvalues with stable asymptotic behaviour. The first is formed by eigenvalues $O(h^2)$ corresponding to the transversal vibrations of the plate with rigidly clamped lateral surface, and the second contains eigenvalues $O(1)$ generated by the longitudinal vibrations of the plate as well as eigen-oscillations of the body without baffle. We verify the convergence theorem for the first series, estimate the errors for both series, and discuss the asymptotic correction terms and boundary layers. Similar but simpler results are obtained in the scalar problem.

Keywords: junction of a massive body and a thin plate, spectrum of an elastic body, asymptotics of eigenvalues and eigenvectors, dimension reduction.

 Funding Agency Grant Number Russian Foundation for Basic Research 12-01-00348

DOI: https://doi.org/10.4213/im7804

Full text: PDF file (1065 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2013, 77:1, 87–142

Bibliographic databases:

Document Type: Article
UDC: 517.956.8+517.956.328+539.3(4)
MSC: 74B05, 74E05, 74H10, 74H45, 74K30
Revised: 12.02.2012

Citation: S. A. Nazarov, “Asymptotics of eigen-oscillations of a massive elastic body with a thin baffle”, Izv. RAN. Ser. Mat., 77:1 (2013), 91–144; Izv. Math., 77:1 (2013), 87–142

Citation in format AMSBIB
\Bibitem{Naz13} \by S.~A.~Nazarov \paper Asymptotics of eigen-oscillations of a~massive elastic body with a~thin baffle \jour Izv. RAN. Ser. Mat. \yr 2013 \vol 77 \issue 1 \pages 91--144 \mathnet{http://mi.mathnet.ru/izv7804} \crossref{https://doi.org/10.4213/im7804} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3087088} \zmath{https://zbmath.org/?q=an:06152571} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2013IzMat..77...87N} \elib{http://elibrary.ru/item.asp?id=20359166} \transl \jour Izv. Math. \yr 2013 \vol 77 \issue 1 \pages 87--142 \crossref{https://doi.org/10.1070/IM2013v077n01ABEH002630} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000315467400005} \elib{http://elibrary.ru/item.asp?id=20442842} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84877049627}