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Zapiski Nauchnykh Seminarov POMI, 2007, Volume 342, Pages 31–76 (Mi znsl121)  
This article is cited in 4 scientific papers (total in 4 papers)

The formal asymptotics of eigenmodes for oscillating elastic spatial body with concentrated masses

D. Gomeza, S. A. Nazarovb, M. E. Perezc

a Departamento de Matemáticas, Estadística y Computación
b Institute of Problems of Mechanical Engineering, Russian Academy of Sciences
c Departamento de Matemática Aplicada y Ciencias de la Computación
Full-text PDF (409 kB) Citations (4)
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Abstract: Limiting spectral problems are derived for the problem about eigen-oscillations of a solid with small heavy (or light) inclusions. The asymptotic ansätze for eigenvalues and eigenvectors as well as the limiting problems are crucially dependent on relation between the geometrical and physical parameters and also the disposition of inclusions. It is established that for heavy inclusions the limiting problems are linked together into the resultant spectral problem which describes “far-action” in the family of the inclusions.
Received: 15.03.2007
English version:
Journal of Mathematical Sciences (New York), 2008, Volume 148, Issue 5, Pages 650–674
DOI: https://doi.org/10.1007/s10958-008-0015-2
Bibliographic databases:
UDC: 517.946
Language: Russian
Citation: D. Gomez, S. A. Nazarov, M. E. Perez, “The formal asymptotics of eigenmodes for oscillating elastic spatial body with concentrated masses”, Mathematical problems in the theory of wave propagation. Part 36, Zap. Nauchn. Sem. POMI, 342, POMI, St. Petersburg, 2007, 31–76; J. Math. Sci. (N. Y.), 148:5 (2008), 650–674
Citation in format AMSBIB
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\by D.~Gomez, S.~A.~Nazarov, M.~E.~Perez
\paper The formal asymptotics of eigenmodes for oscillating elastic spatial body with concentrated masses
\inbook Mathematical problems in the theory of wave propagation. Part~36
\serial Zap. Nauchn. Sem. POMI
\yr 2007
\vol 342
\pages 31--76
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl121}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2365108}
\zmath{https://zbmath.org/?q=an:05637555}
\elib{https://elibrary.ru/item.asp?id=9593776}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2008
\vol 148
\issue 5
\pages 650--674
\crossref{https://doi.org/10.1007/s10958-008-0015-2}
\elib{https://elibrary.ru/item.asp?id=13571059}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-38349115609}
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    • 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
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