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Algebra i Analiz, 2020, Volume 32, Issue 3, Pages 219–237 (Mi aa1706)  
This article is cited in 6 scientific papers (total in 6 papers)

Research Papers

On meso-scale approximations for vibrations of membranes with lower-dimensional clusters of inertial inclusions

V. G. Maz'yaabc, A. B. Movchanb, M. J. Nievesde

a Department of Mathematics, Linköping University, Linköping S--581 83, Sweden
b Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK
c RUDN University, 6 Miklukho-Maklay St, 117198 Moscow, Russia
d School of Computing and Mathematics, Keele University, Staffordshire, ST5 5BG, UK
e Department of Mechanical, Chemical and Material Engineering, University of Cagliari, 09123 Cagliari, Italy
Full-text PDF (420 kB) Citations (6)
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Abstract: Formal asymptotic algorithms are considered for a class of meso-scale approximations for problems of vibration of elastic membranes that contain clusters of small inertial inclusions distributed along contours of predefined smooth shapes. Effective transmission conditions have been identified for inertial structured interfaces, and approximations to solutions of eigenvalue problems have been derived for domains containing lower-dimensional clusters of inclusions.
Keywords: two-dimensional elastic membranes, clusters of small inclusions, inertia of inclusions.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation
Engineering and Physical Sciences Research Council EP/L024926/1
EU Framework Programme for Research and Innovation MSCA-IF-2016-747334-CAT-FFLAP
V.G.M. acknowledges that this publication has been prepared with the support of the “RUDN University Program 5-100.” A.B.M would like to thank the EPSRC (UK) for its support through the Programme Grant №EP/L024926/1. M.J.N gratefully acknowledges the support of the EU H2020 grant MSCA-IF-2016-747334-CAT-FFLAP.
Received: 11.05.2019
English version:
St. Petersburg Mathematical Journal, 2021, Volume 32, Issue 3, Pages 551–564
DOI: https://doi.org/10.1090/spmj/1661
Document Type: Article
Language: English
Citation: V. G. Maz'ya, A. B. Movchan, M. J. Nieves, “On meso-scale approximations for vibrations of membranes with lower-dimensional clusters of inertial inclusions”, Algebra i Analiz, 32:3 (2020), 219–237; St. Petersburg Math. J., 32:3 (2021), 551–564
Citation in format AMSBIB
\Bibitem{MazMovNie20}
\by V.~G.~Maz'ya, A.~B.~Movchan, M.~J.~Nieves
\paper On meso-scale approximations for vibrations of membranes with lower-dimensional clusters of inertial inclusions
\jour Algebra i Analiz
\yr 2020
\vol 32
\issue 3
\pages 219--237
\mathnet{http://mi.mathnet.ru/aa1706}
\transl
\jour St. Petersburg Math. J.
\yr 2021
\vol 32
\issue 3
\pages 551--564
\crossref{https://doi.org/10.1090/spmj/1661}
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и анализ St. Petersburg Mathematical Journal
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    Full-text PDF :16
    References:28
    First page:18
     
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