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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Volume 295, Pages 218–228
DOI: https://doi.org/10.1134/S0371968516040130
(Mi tm3762)
 

This article is cited in 18 scientific papers (total in 18 papers)

Asymptotic behavior of the spectrum of one-dimensional vibrations in a layered medium consisting of elastic and Kelvin–Voigt viscoelastic materials

A. S. Shamaev, V. V. Shumilova

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
References:
Abstract: The work is devoted to the analysis of the spectral properties of a boundary value problem describing one-dimensional vibrations along the axis Ox1 of periodically alternating M elastic and M viscoelastic layers parallel to the plane Ox2x3. It is shown that the spectrum of the boundary value problem is the union of roots of M equations. The asymptotic behavior of the spectrum of the problem as M is analyzed; in particular, it is proved that not all sequences of eigenvalues of the original (prelimit) problem converge to eigenvalues of the corresponding homogenized (limit) problem.
Funding agency Grant number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.
Received: June 22, 2016
English version:
Proceedings of the Steklov Institute of Mathematics, 2016, Volume 295, Pages 202–212
DOI: https://doi.org/10.1134/S0081543816080137
Bibliographic databases:
Document Type: Article
UDC: 517.958+517.984
Language: Russian
Citation: A. S. Shamaev, V. V. Shumilova, “Asymptotic behavior of the spectrum of one-dimensional vibrations in a layered medium consisting of elastic and Kelvin–Voigt viscoelastic materials”, Modern problems of mechanics, Collected papers, Trudy Mat. Inst. Steklova, 295, MAIK Nauka/Interperiodica, Moscow, 2016, 218–228; Proc. Steklov Inst. Math., 295 (2016), 202–212
Citation in format AMSBIB
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\inbook Modern problems of mechanics
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
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\vol 295
\pages 218--228
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • This publication is cited in the following 18 articles:
    1. A. S. Shamaev, V. V. Shumilova, “Homogenization of motion equations for medium consisting of elastic material and incompessible Kelvin-Voigt fluid”, Ufa Math. J., 16:1 (2024), 100–111  mathnet  crossref
    2. Vladlena V. Shumilova, “Spectrum of one-dimensional eigenoscillations of two-phase layered composites”, Zhurn. SFU. Ser. Matem. i fiz., 16:1 (2023), 35–47  mathnet  mathscinet
    3. Tatiana Bobyleva, Alexey Shamaev, A. Ter-Martirosyan, D. Bazarov, “On the spectra of composite materials with different dissipation models”, E3S Web of Conf., 410 (2023), 01004  crossref
    4. Tatyana Bobyleva, Alexey Shamaev, Lecture Notes in Civil Engineering, 282, Proceedings of FORM 2022, 2023, 211  crossref
    5. V. V. Shumilova, “Spektr odnomernykh sobstvennykh kolebanii dvukhfaznykh sloistykh sred s periodicheskoi strukturoi”, Tr. IMM UrO RAN, 28, no. 4, 2022, 250–261  mathnet  crossref  mathscinet  elib
    6. A. S. Shamaev, V. V. Shumilova, “Spectrum of One-Dimensional Eigenoscillations of a Medium Consisting of Viscoelastic Material with Memory and Incompressible Viscous Fluid”, J Math Sci, 257:5 (2021), 732  crossref
    7. V. V. Shumilova, “Spektr sobstvennykh kolebanii sloistoi sredy, sostoyaschei iz materiala Kelvina–Foigta i vyazkoi neszhimaemoi zhidkosti”, Sib. elektron. matem. izv., 17 (2020), 21–31  mathnet  crossref
    8. A. S. Shamaev, V. V. Shumilova, “Spectrum of one-dimensional natural vibrations of layered medium consisting of elastic material and viscous incompressible fluid”, Moscow University Mathematics Bulletin, 75:4 (2020), 172–176  mathnet  crossref  mathscinet  zmath  isi
    9. A. S. Shamaev, V. V. Shumilova, “Asymptotics of the Spectra of One-Dimensional Natural Vibrations in Media Consisting of Solid and Fluid Layers”, Dokl. Phys., 65:4 (2020), 153  crossref
    10. T N Bobyleva, A S Shamaev, “Effective modules of a layered elastic creep medium with power creep kernels”, IOP Conf. Ser.: Mater. Sci. Eng., 913:3 (2020), 032059  crossref
    11. A. S. Shamaev, V. V. Shumilova, “Asymptotics of the spectrum of one-dimensional natural vibrations in a layered medium consisting of viscoelastic material and viscous fluid”, Fluid Dyn., 54:6 (2019), 749–760  crossref  mathscinet  zmath  isi  scopus
    12. Tatyana Bobyleva, Tat'yana Bobyleva, “AVERAGED MODEL OF LAYERED ELASTIC-CREEPING COMPOSITE MATERI-ALS”, Bulletin of Belgorod State Technological University named after. V. G. Shukhov, 4:1 (2019), 45  crossref
    13. A. S. Shamaev, V. V. Shumilova, “Calculation of natural frequencies and damping coefficients of a multi-layered composite using homogenization theory”, IFAC-PapersOnLine, 51:2 (2018), 126–131  crossref  isi  scopus
    14. T. N. Bobyleva, A. S. Shamaev, “Method of approximate calculation of the stress tensor in layered elastic-creeping environments”, IFAC-PapersOnLine, 51:2 (2018), 138–143  crossref  isi  scopus
    15. T. Bobyleva, A. Shamaev, “The averaged model of layered elastic-creeping composite materials”, XXI International Scientific Conference on Advanced in Civil Engineering Construction - the Formation of Living Environment, IOP Conference Series-Materials Science and Engineering, 365, ed. y A. Askadskiy, A. Pustovgar, T. Matseevich, A. Adamtsevich, IOP Publishing Ltd, 2018, 042078  crossref  isi  scopus
    16. Tatiana Bobyleva, Alexei Shamaev, A. Volkov, A. Pustovgar, A. Adamtsevich, “Effective characteristics of a layered tube consisting of elastic-creeping materials”, MATEC Web Conf., 251 (2018), 04039  crossref
    17. T. Bobyleva, A. Shamaev, “Stress distribution in layered elastic creeping array with a vertical cylindrical shaft”, RSP 2017 (XXVI R-S-P Seminar 2017 Theoretical Foundation of Civil Engineering), MATEC Web Conf., 117, ed. S. Jemiolo, A. Zbiciak, M. MitewCzajewska, M. Krzeminski, M. Gajewski, EDP Sciences, 2017, UNSP 00020  crossref  isi  scopus
    18. T. N. Bobyleva, “Method of calculation of stresses in the layered elastic-creeping arrays”, 5th International Scientific Conference Integration, Partnership and Innovation in Construction Science and Education, MATEC Web Conf., 86, ed. V. Andreev, EDP Sciences, 2016, UNSP 01024  crossref  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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