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Asymptotic structure of the spectrum of a thin Dirichlet single-tee beam
- Authors: Nazarov S.A.1
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Affiliations:
- Institute of Mechanical Engineering Problems of the Russian Academy of Sciences
- Issue: Vol 518, No 1 (2024)
- Pages: 57-63
- Section: МЕХАНИКА
- URL: https://ruspoj.com/2686-7400/article/view/677507
- DOI: https://doi.org/10.31857/S2686740024050094
- EDN: https://elibrary.ru/HXJICG
- ID: 677507
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Abstract
The asymptotic behaviour of eigenvalues and eigenfunctions of the Dirichlet problem for the Laplace operator in a tee-type junction of two thin parallelepiped plates is examined. The effect of a strong localization is observed for eigenfunctions near junction zones. Comparing with asymptotic results for analogous Neumann problem, the crucial difference between asymptotic behaviour of their spectra is observed.
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About the authors
S. A. Nazarov
Institute of Mechanical Engineering Problems of the Russian Academy of Sciences
Author for correspondence.
Email: srgnazarov@yahoo.co.uk
Russian Federation, Saint-Petersburg
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Fig. 1. Three-dimensional (a) and two-dimensional (b) articulations.
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Fig. 2. T-shaped waveguide (a). Half-strip with a beveled end (b) – letters D and N indicate the type of boundary condition on the sides and end.
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Fig. 3. Beveled single-T beam (a) and straight I-beam (b).
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