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Zap. Nauchn. Sem. POMI, 2007, Volume 342, Pages 31–76 (Mi znsl121)  

This article is cited in 2 scientific papers (total in 2 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

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.

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English version:
Journal of Mathematical Sciences (New York), 2008, 148:5, 650–674

Bibliographic databases:

UDC: 517.946
Received: 15.03.2007

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://www.ams.org/mathscinet-getitem?mr=2365108}
\zmath{https://zbmath.org/?q=an:05637555}
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\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{http://elibrary.ru/item.asp?id=13571059}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-38349115609}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Nazarov S.A., Sokolowski J., “On asymptotic analysis of spectral problems in elasticity”, Latin American Journal of Solids and Structures, 8:1 (2011), 27–54  crossref  mathscinet  isi  scopus
    2. S. E. Kholodovskii, “Effective solution of the problem of motion of an infinite string with an attached point mass”, Comput. Math. Math. Phys., 55:1 (2015), 101–108  mathnet  crossref  crossref  mathscinet  isi  elib  elib
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