Asymptotic analysis of high frequency modes for thin elastic plates

Nabil Kerdid; Nabil Kerdid

doi:10.3934/math.2023948

AIMS Mathematics

2023, Volume 8, Issue 8: 18618-18630. doi: 10.3934/math.2023948

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Research article

Asymptotic analysis of high frequency modes for thin elastic plates

Nabil Kerdid ^,

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

Received: 07 March 2023 Revised: 15 May 2023 Accepted: 21 May 2023 Published: 02 June 2023
MSC : 35E20, 35C20, 74B05, 74K20, 74G10

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.
- linear elasticity,
- asymptotic analysis,
- thin plates,
- eigenvalue problem,
- high frequency modes,
- stretching vibrations
Citation: Nabil Kerdid. Asymptotic analysis of high frequency modes for thin elastic plates[J]. AIMS Mathematics, 2023, 8(8): 18618-18630. doi: 10.3934/math.2023948

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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.

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