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

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Sibirskii Zhurnal Industrial'noi Matematiki, 2012, Volume 15, Number 4, Pages 124–134 (Mi sjim759)

This article is cited in 12 scientific papers (total in 12 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

Full-text PDF (242 kB) Citations (12)

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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.

Received: 11.05.2012

Document Type: Article

UDC: 517.958+534.18

Language: Russian

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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https://www.mathnet.ru/eng/sjim759

https://www.mathnet.ru/eng/sjim/v15/i4/p124

This publication is cited in the following 12 articles:

Shamaev A.S., Shumilova V.V., “Effective Acoustic Equations For a Layered Material Described By the Fractional Kelvin-Voigt Model”, J. Sib. Fed. Univ.-Math. Phys., 14:3 (2021), 351–359
Shamaev A.S., Shumilova V.V., “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
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
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
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
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
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
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
A. S. Shamaev, V. V. Shumilova, “Transmission of a plane acoustic wave through a composite consisting of elastic and viscoelastic layers”, Dokl. Phys., 60:7 (2015), 305–309
V. V. Shumilova, “Homogenization of the acoustic equations for a medium consisting of a viscoelastic material and a slightly viscous compressible liquid”, Differ. Equ., 51:4 (2015), 566–570
Sorokin V.S., “Homogenization of One-Dimensional Oscillatory Systems With Spatially Modulated Parameters”, Pmm-J. Appl. Math. Mech., 78:3 (2014), 242–248
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Сибирский журнал индустриальной математики

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