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Sib. Zh. Ind. Mat., 2012, Volume 15, Number 4, Pages 124–134 (Mi sjim759)  

This article is cited in 10 scientific papers (total in 10 papers)

On the spectrum of one-dimensional oscillations of a laminated composite with components of elastic and viscoelastic materials

A. S. Shamaev, V. V. Shumilova

Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia

Abstract: We construct two averaged (effective) models corresponding to transverse and longitudinal oscillations of a laminated composite. The components of such a composite are mutually alternating layers of isotropic elastic and viscoelastic materials. We prove that the study of the spectrum of each of the averaged models is reduced to finding the roots of the corresponding linear fractional equations.

Keywords: oscillation spectrum, laminated composite, elasticity, viscoelasticity, averaged model.

Full text: PDF file (242 kB)
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UDC: 517.958+534.18
Received: 11.05.2012

Citation: A. S. Shamaev, V. V. Shumilova, “On the spectrum of one-dimensional oscillations of a laminated composite with components of elastic and viscoelastic materials”, Sib. Zh. Ind. Mat., 15:4 (2012), 124–134

Citation in format AMSBIB
\Bibitem{ShaShu12}
\by A.~S.~Shamaev, V.~V.~Shumilova
\paper On the spectrum of one-dimensional oscillations of a~laminated composite with components of elastic and viscoelastic materials
\jour Sib. Zh. Ind. Mat.
\yr 2012
\vol 15
\issue 4
\pages 124--134
\mathnet{http://mi.mathnet.ru/sjim759}


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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. 60, no. 7, 2015, 305–309  crossref  isi  elib  scopus
    2. 51, no. 4, 2015, 566–570  crossref  zmath  isi  elib  scopus
    3. Vladlena V. Shumilova, “Spectrum of One-dimensional Vibrations of a Layered Medium Consisting of a Kelvin–Voigt Material and a Viscous Incompressible Fluid”, Zhurn. SFU. Ser. Matem. i fiz., 6:3 (2013), 349–356  mathnet
    4. Sorokin V.S., “Homogenization of One-Dimensional Oscillatory Systems With Spatially Modulated Parameters”, Pmm-J. Appl. Math. Mech., 78:3 (2014), 242–248  crossref  isi  scopus
    5. V. V. Shumilova, “Reflection of a plane sound wave from the boundary of a heterogeneous medium consisting of elastic and viscoelastic layers”, Comput. Math. Math. Phys., 55:7 (2015), 1188–1199  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    6. Shamaev A.S., Shumilova V.V., “Passage of a Plane Acoustic Wave Through a Layered Composite With Components of Elastic and Viscoelastic Materials”, Acoust. Phys., 61:1 (2015), 8–18  crossref  isi  elib  scopus
    7. A. S. Shamaev, V. V. Shumilova, “Homogenization of the equations of state for a heterogeneous layered medium consisting of two creep materials”, Proc. Steklov Inst. Math., 295 (2016), 213–224  mathnet  crossref  crossref  mathscinet  isi  elib
    8. T. N. Bobyleva, A. S. Shamaev, “An efficient algorithm for calculating rheological parameters of layered soil media composed from elastic-creeping materials”, Soil Mech. Found. Eng., 54:4 (2017), 224–230  crossref  isi  scopus
    9. A. S. Shamaev, V. V. Shumilova, “Plane acoustic wave propagation through a composite of elastic and Kelvin-Voigt viscoelastic material layers”, Mech. Sol., 52:1 (2017), 25–34  crossref  mathscinet  isi  scopus
    10. Shamaev A.S., Shumilova V.V., “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
  • Сибирский журнал индустриальной математики
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