High-frequency cell vibrations and spatial skin effect in thick cascade junction with heavy concentrated masses |
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| Authors: | Gregory A. Chechkin Taras A. Mel'nyk |
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| Affiliation: | 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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| Abstract: | 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 ε→0, 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. |
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| Keywords: | Asymptotic expansion Spectral problem Thick cascade junction Domain with highly oscillating boundary Concentrated masses |
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