Comptes Rendus
High-frequency cell vibrations and spatial skin effect in thick cascade junction with heavy concentrated masses
Comptes Rendus. Mécanique, Volume 342 (2014) no. 4, pp. 221-228.

We study the asymptotic behavior of eigenvalues and eigenfunctions of the Laplacian in a 2D thick cascade junction with heavy concentrated masses. We present two-term asymptotic approximations, as ε0, for the eigenelements in the case of “slightly heavy”, “moderate heavy”, and “super heavy” concentrated masses. Asymptotics of high-frequency cell-vibrations are found as well.

Nous étudions le comportement asymptotique des valeurs et fonctions propres du laplacien dans une jonction cascade épaisse bidimensionnelle, avec des masses lourdes concentrées. Si ε0, nous présentons des approximations asymptotiques en deux termes pour les éléments propres dans les cas des masses concentrées « peu lourdes », « modérément lourdes » et « super-lourdes ». L'analyse asymptotique pour les vibrations à haute fréquence cellulaire est aussi trouvée.

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Published online:
DOI: 10.1016/j.crme.2014.01.002
Keywords: Asymptotic expansion, Spectral problem, Thick cascade junction, Domain with highly oscillating boundary, Concentrated masses
Mot clés : Développement asymptotique, Problème spectral, Jonction cascade épaisse, Domaine avec oscillation forte du bord, Masses concentrées
Gregory A. Chechkin 1; Taras A. Mel'nyk 2

1 Department of Differential Equations, Faculty of Mechanics and Mathematics, M.V. Lomonosov Moscow State University, Moscow 119991, Russia
2 Department of Mathematical Physics, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska st., 64/13, Kyiv 01601, Ukraine
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Gregory A. Chechkin; Taras A. Mel'nyk. High-frequency cell vibrations and spatial skin effect in thick cascade junction with heavy concentrated masses. Comptes Rendus. Mécanique, Volume 342 (2014) no. 4, pp. 221-228. doi : 10.1016/j.crme.2014.01.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.01.002/

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