Waves Trapped by Semi-Infinite Kirchhoff Plate at Ultra-Low Frequencies

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Waves Trapped by Semi-Infinite Kirchhoff Plate at Ultra-Low Frequencies. / Nazarov, S. A.

In: Mechanics of Solids, Vol. 55, No. 8, 12.2020, p. 1328-1339.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{135e22d7120248f3b4c469ec927530a4,

title = "Waves Trapped by Semi-Infinite Kirchhoff Plate at Ultra-Low Frequencies",

abstract = "Abstract: In this paper, a semi-infinite Kirchhoff plate with a traction-free edge, which rests partially on a heterogeneous Winkler foundation (the Neumann problem for the biharmonic operator perturbed by a small free term with a compact support), is considered. It is shown that, for arbitrary small ε > 0, a variable foundation compliance coefficient (defined nonuniquely) of order ε can be constructed, such that the plate obtains the eigenvalue ε4 that is embedded into a continuous spectrum, and the corresponding eigenfunction decays exponentially at infinity. It is verified that no more than one small eigenvalue can exist. It is noteworthy that a small perturbation cannot prompt an emergence of an eigenvalue near the cutoff point of the continuous spectrum in an acoustic waveguide (the Neumann problem for the Laplace operator).",

keywords = "near-threshold eigenvalue embedded into continuous spectrum, semi-infinite Kirchhoff plate, small perturbation, threshold resonance, Winkler foundation",

author = "Nazarov, {S. A.}",

note = "Publisher Copyright: {\textcopyright} 2020, Allerton Press, Inc.",

year = "2020",

month = dec,

doi = "10.3103/S002565442008018X",

language = "English",

volume = "55",

pages = "1328--1339",

journal = "Mechanics of Solids",

issn = "0025-6544",

publisher = "Allerton Press, Inc.",

number = "8",

}

RIS

TY - JOUR

T1 - Waves Trapped by Semi-Infinite Kirchhoff Plate at Ultra-Low Frequencies

AU - Nazarov, S. A.

PY - 2020/12

Y1 - 2020/12

N2 - Abstract: In this paper, a semi-infinite Kirchhoff plate with a traction-free edge, which rests partially on a heterogeneous Winkler foundation (the Neumann problem for the biharmonic operator perturbed by a small free term with a compact support), is considered. It is shown that, for arbitrary small ε > 0, a variable foundation compliance coefficient (defined nonuniquely) of order ε can be constructed, such that the plate obtains the eigenvalue ε4 that is embedded into a continuous spectrum, and the corresponding eigenfunction decays exponentially at infinity. It is verified that no more than one small eigenvalue can exist. It is noteworthy that a small perturbation cannot prompt an emergence of an eigenvalue near the cutoff point of the continuous spectrum in an acoustic waveguide (the Neumann problem for the Laplace operator).

AB - Abstract: In this paper, a semi-infinite Kirchhoff plate with a traction-free edge, which rests partially on a heterogeneous Winkler foundation (the Neumann problem for the biharmonic operator perturbed by a small free term with a compact support), is considered. It is shown that, for arbitrary small ε > 0, a variable foundation compliance coefficient (defined nonuniquely) of order ε can be constructed, such that the plate obtains the eigenvalue ε4 that is embedded into a continuous spectrum, and the corresponding eigenfunction decays exponentially at infinity. It is verified that no more than one small eigenvalue can exist. It is noteworthy that a small perturbation cannot prompt an emergence of an eigenvalue near the cutoff point of the continuous spectrum in an acoustic waveguide (the Neumann problem for the Laplace operator).

KW - near-threshold eigenvalue embedded into continuous spectrum

KW - semi-infinite Kirchhoff plate

KW - small perturbation

KW - threshold resonance

KW - Winkler foundation

UR - http://www.scopus.com/inward/record.url?scp=85101746780&partnerID=8YFLogxK

U2 - 10.3103/S002565442008018X

DO - 10.3103/S002565442008018X

M3 - Article

AN - SCOPUS:85101746780

VL - 55

SP - 1328

EP - 1339

JO - Mechanics of Solids

JF - Mechanics of Solids

SN - 0025-6544

IS - 8

ER -

ID: 88366220