Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2020), pp. 53-57
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A. S. Shamaev; V. V. Shumilova. Spectrum of one-dimensional natural vibrations of layered medium consisting of elastic material and viscous incompressible fluid. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2020), pp. 53-57. http://geodesic.mathdoc.fr/item/VMUMM_2020_4_a7/
@article{VMUMM_2020_4_a7,
author = {A. S. Shamaev and V. V. Shumilova},
title = {Spectrum of one-dimensional natural vibrations of layered medium consisting of elastic material and viscous incompressible fluid},
journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
pages = {53--57},
year = {2020},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMUMM_2020_4_a7/}
}
TY - JOUR
AU - A. S. Shamaev
AU - V. V. Shumilova
TI - Spectrum of one-dimensional natural vibrations of layered medium consisting of elastic material and viscous incompressible fluid
JO - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY - 2020
SP - 53
EP - 57
IS - 4
UR - http://geodesic.mathdoc.fr/item/VMUMM_2020_4_a7/
LA - ru
ID - VMUMM_2020_4_a7
ER -
%0 Journal Article
%A A. S. Shamaev
%A V. V. Shumilova
%T Spectrum of one-dimensional natural vibrations of layered medium consisting of elastic material and viscous incompressible fluid
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2020
%P 53-57
%N 4
%U http://geodesic.mathdoc.fr/item/VMUMM_2020_4_a7/
%G ru
%F VMUMM_2020_4_a7
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 is studied. 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.
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[2] 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 | DOI
[3] Gilbert R. P., Mikelić A., “Homogenizing the acoustic properties of the seabed: Part I”, Nonlinear Analysis, 40 (2000), 185–212 | DOI | MR | Zbl
[4] Oleinik O. A., Iosifyan G. A., Shamaev A. S., Matematicheskie zadachi teorii silno neodnorodnykh uprugikh sred, Izd-vo MGU, M., 1990 | MR
