Asymptotic analysis of stretching modes for a folded plate

Nabil Kerdid; Nabil Kerdid

doi:10.3934/math.20231222

AIMS Mathematics

2023, Volume 8, Issue 10: 23974-23988. doi: 10.3934/math.20231222

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Research article

Asymptotic analysis of stretching modes for a folded plate

Nabil Kerdid ^,

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

Received: 01 June 2023 Revised: 18 July 2023 Accepted: 26 July 2023 Published: 07 August 2023
MSC : 35C20, 35E20, 74B05, 74G10, 74K20

In this paper, we show that the spectral problem associated to stretching modes in a thin folded plate can be derived from the three-dimensional eigenvalue problem of linear elasticity through a rigourous convergence analysis as the thickness of the plate goes to zero. We show, using a nonstandard asymptotic analysis technique, that each stretching frequency of an elastic thin folded plate is the limit of a family of high frequencies of the three-dimensional linearized elasticity system in the folded plate, as the thickness approaches zero.
- linear elasticity,
- asymptotic analysis,
- stretching modes,
- folded plate,
- eigenvalue problem
Citation: Nabil Kerdid. Asymptotic analysis of stretching modes for a folded plate[J]. AIMS Mathematics, 2023, 8(10): 23974-23988. doi: 10.3934/math.20231222

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Abstract

In this paper, we show that the spectral problem associated to stretching modes in a thin folded plate can be derived from the three-dimensional eigenvalue problem of linear elasticity through a rigourous convergence analysis as the thickness of the plate goes to zero. We show, using a nonstandard asymptotic analysis technique, that each stretching frequency of an elastic thin folded plate is the limit of a family of high frequencies of the three-dimensional linearized elasticity system in the folded plate, as the thickness approaches zero.

References

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