dc.contributor.author Čečkin, Grigorij A. dc.contributor.author Mel'nyk, Taras A. dc.date.accessioned 2013-12-13T12:00:00Z dc.date.accessioned 2016-10-05T14:13:57Z dc.date.available 2013-12-13T12:00:00Z dc.date.available 2016-10-05T14:13:57Z dc.date.issued 2013-12-13 dc.identifier.uri http://publications.mfo.de/handle/mfo/1073 dc.description Research in Pairs 2013 en_US dc.description.abstract The asymptotic behavior (as $\varepsilon \to 0$) of eigenvalues and eigenfunctions of a boundary-value problem for the Laplace operator in a thick cascade junction with concentrated masses is studied. This cascade junction consists of the junction’s body and a great number $5N= \mathcal{O}(\varepsilon^{-1})$ of $\varepsilon$-alternating thin rods belonging to two classes. One class consists of rods of finite length and the second one consists of rods of small length of order $\mathcal{O}(\varepsilon)$. The mass density is of order $\mathcal{O}(\varepsilon^{-\alpha})$ on the rods from the second class and $\mathcal{O}(1)$ outside of them. There exist five qualitatively different cases in the asymptotic behavior of eigen-magnitudes as $\varepsilon \to 0$, namely the case of “light” concentrated masses $(a \in (0,1))$, “intermediate” concentrated masses $(\alpha=1)$ and “heavy” concentrated masses ($\alpha \in (1, +\infty")$) that we divide into “slightly heavy” concentrated masses ($\alpha \in (1,2)$), “moderate heavy” concentrated masses ($\alpha=2$), and “super heavy” concentrated masses ($alpha>2$). In the paper we study the influence of the concentrated masses on the asymptotic behavior of the eigen-magnitudes in the cases $\alpha=2$ and $\alpha>2$. The leading terms of asymptotic expansions both for the eigenvalues and eigenfunctions are constructed and the corresponding asymptotic estimates are proved. In addition, a new kind of high-frequency vibrations is found. en_US dc.language.iso en en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2013,26 dc.title Enhanced Spatial Skin-Effect for Free Vibrations of a Thick Cascade Junction with "Super Heavy" Concentrated Masses en_US dc.type Preprint en_US dc.identifier.doi 10.14760/OWP-2013-26 local.scientificprogram Research in Pairs 2013 local.series.id OWP-2013-26
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