Asymptotic behavior of the eigenfrequencies of a thin elastic rod with non-uniform cross-section of extremely oblate shape

Jimbo, Shuichi; Ushikoshi, Erika; Yoshihara, Hiromasa

doi:10.1007/s00526-022-02325-1

Calc. Var.

2022

DOI: 10.1007/s00526-022-02325-1

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Asymptotic behavior of the eigenfrequencies of a thin elastic rod with non-uniform cross-section of extremely oblate shape

Shuichi Jimbo

Erika Ushikoshi

Hiromasa Yoshihara

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2023

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Cited by 2 publications

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Asymptotic analysis of stretching modes for a folded plate

Kerdid

2023

MATH

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<abstract><p>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.</p></abstract>

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Asymptotic analysis of stretching modes for a folded plate

Kerdid

2023

MATH

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Asymptotic analysis of high frequency modes for thin elastic plates

Kerdid

2023

MATH

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Asymptotic behavior of the eigenfrequencies of a thin elastic rod with non-uniform cross-section of extremely oblate shape

Cited by 2 publications

References 18 publications

Asymptotic analysis of stretching modes for a folded plate

Asymptotic analysis of stretching modes for a folded plate

Asymptotic analysis of high frequency modes for thin elastic plates

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