Spectrum of One-Dimensional Natural Vibrations of Layered Medium Consisting of Elastic Material and Viscous Incompressible Fluid

The article considers the spectrum of one-dimensional natural vibrations of a layered medium with a periodic structure consisting of an isotropic elastic material and a viscous incompressible fluid. It is established that the spectrum points are the roots of transcendental equations. In order to sol...

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Bibliographic Details
Published inMoscow University mathematics bulletin Vol. 75; no. 4; pp. 172 - 176
Main Authors Shamaev, A. S., Shumilova, V. V.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.07.2020
Springer Nature B.V
Subjects
Analysis
Computational fluid dynamics
Fluid flow
Incompressible flow
Incompressible fluids
Isotropic material
Mathematical analysis
Mathematics
Mathematics and Statistics
Multilayers
Periodic structures
Quadratic equations
spectrum
natural vibrations
layered medium
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Summary:The article considers the spectrum of one-dimensional natural vibrations of a layered medium with a periodic structure consisting of an isotropic elastic material and a viscous incompressible fluid. It is established that the spectrum points are the roots of transcendental equations. In order to solve these equations numerically for multi-layered media, the roots of quadratic equations are proposed to use as initial approximations.
ISSN:0027-1322
1934-8444
DOI:10.3103/S0027132220040063