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Asymptotic analysis of the high frequencies for the Laplace operator in a thin T-like shaped structure

Abstract: We consider a spectral problem for the Laplacian operator in a planar T-like shaped thin structure , where E; denotes the transversal thickness of both branches. We assume the homogeneous Dirichlet boundary condition on the ends of the branches and the homogeneous Neumann boundary condition on the remaining part of the boundary of . We study the asymptotic behavior, as ; tends to zero, of the high frequencies of such a problem. Unlike the asymptotic behavior of the low frequencies where the limit problem involves only longitudinal vibrations along each branch of the T-like shaped thin structure (i.e. 1D limit spectral problems), we obtain a two dimensional limit spectral problem which allows us to capture other kinds of vibrations. We also give a characterization of the asymptotic form of the eigenfunctions originating these vibrations.

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

 Fuente: Journal de Mathématiques Pures et Appliquées Volume 134, February 2020, Pages 299-327

Editorial: Elsevier

 Fecha de publicación: 28/06/2019

Nº de páginas: 32

Tipo de publicación: Artículo de Revista

 DOI: 10.1016/j.matpur.2019.06.005

ISSN: 1776-3371,0021-7824

Proyecto español: MTM2013-44883-P

Url de la publicación: https://doi.org/10.1016/j.matpur.2019.06.005