Abstract:
The paper is devoted to the construction of effective acoustic equations for a two-phase layered viscoelastic material described by the Kelvin–Voigt model with fractional time derivatives. For this purpose, the theory of two-scale convergence and the Laplace transform with respect to time are used. It is shown that the effective equations are partial integro-differential equations with fractional time derivatives and fractional exponential convolution kernels. In order to find the coefficients and the convolution kernels of these equations, several auxiliary cell problems are formulated and solved.
Received: 10.12.2020 Received in revised form: 16.01.2021 Accepted: 05.03.2021
Bibliographic databases:
Document Type:
Article
UDC:
534.18
Language: English
Citation:
Alexey S. Shamaev, Vladlena V. Shumilova, “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
\Bibitem{ShaShu21}
\by Alexey~S.~Shamaev, Vladlena~V.~Shumilova
\paper Effective acoustic equations for a layered material described by the fractional Kelvin--Voigt model
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2021
\vol 14
\issue 3
\pages 351--359
\mathnet{http://mi.mathnet.ru/jsfu919}
\crossref{https://doi.org/10.17516/1997-1397-2021-14-3-351-359}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000658493100008}
Linking options:
https://www.mathnet.ru/eng/jsfu919
https://www.mathnet.ru/eng/jsfu/v14/i3/p351
This publication is cited in the following 2 articles:
A. S. Shamaev, V. V. Shumilova, “Spectrum of an Integro-Differential Equation of Fractional Order”, J Math Sci, 276:1 (2023), 191
Shitikova M.V., “Fractional Operator Viscoelastic Models in Dynamic Problems of Mechanics of Solids: a Review”, Mech. Sol., 57:1 (2022), 1–33
Citation in format AMSBIB
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