Geodesic
Asymptotic behavior of the spectrum of one-dimensional vibrations in a~layered medium consisting of elastic and Kelvin--Voigt viscoelastic materials
Informatics and Automation, Modern problems of mechanics, Tome 295 (2016), pp. 218-228

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The work is devoted to the analysis of the spectral properties of a boundary value problem describing one-dimensional vibrations along the axis $Ox_1$ of periodically alternating $M$ elastic and $M$ viscoelastic layers parallel to the plane $Ox_2x_3$. It is shown that the spectrum of the boundary value problem is the union of roots of $M$ equations. The asymptotic behavior of the spectrum of the problem as $M\to\infty$ is analyzed; in particular, it is proved that not all sequences of eigenvalues of the original (prelimit) problem converge to eigenvalues of the corresponding homogenized (limit) problem. 
@article{TRSPY_2016_295_a12,
     author = {A. S. Shamaev and V. V. Shumilova},
     title = {Asymptotic behavior of the spectrum of one-dimensional vibrations in a~layered medium consisting of elastic and {Kelvin--Voigt} viscoelastic materials},
     journal = {Informatics and Automation},
     pages = {218--228},
     publisher = {mathdoc},
     volume = {295},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2016_295_a12/}
}
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A. S. Shamaev; V. V. Shumilova. Asymptotic behavior of the spectrum of one-dimensional vibrations in a~layered medium consisting of elastic and Kelvin--Voigt viscoelastic materials. Informatics and Automation, Modern problems of mechanics, Tome 295 (2016), pp. 218-228. http://geodesic.mathdoc.fr/item/TRSPY_2016_295_a12/