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Research Article | Open Access

Asymptotic analysis of high frequency modes for thin elastic plates

Department of Mathematics and Statistics, College of Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 90950, Riyadh 11623, Saudi Arabia
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Abstract

In this paper, we show that the high frequency modes of a thin clamped plate and the associated eigenfunctions converge, as the thickness of the plate goes to zero, to the eigenvalues and the eigenfunctions of a two-dimensional eigenvalue problem associated to the stretching displacements of the plate.

Keywords

linear elasticityasymptotic analysisthin plateseigenvalue problemhigh frequency modesstretching vibrations
CLC number: 35E20, 35C20, 74B05, 74K20, 74G10

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AIMS Mathematics
Volume 8 Issue 8,
August 2023
Pages 18618-18630
DOI: 10.3934/math.2023948

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Cite this article:
Kerdid N. Asymptotic analysis of high frequency modes for thin elastic plates. AIMS Mathematics, 2023, 8(8): 18618-18630. https://doi.org/10.3934/math.2023948

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Received: 07 March 2023
Revised: 15 May 2023
Accepted: 21 May 2023
Published: 15 August 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)