Constructing a Trapped Mode at Low Frequencies in an Elastic Waveguide

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Constructing a Trapped Mode at Low Frequencies in an Elastic Waveguide. / Nazarov, S. A.

In: Functional Analysis and its Applications, Vol. 54, No. 1, 01.2020, p. 31-44.

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Nazarov, S. A. / Constructing a Trapped Mode at Low Frequencies in an Elastic Waveguide. In: Functional Analysis and its Applications. 2020 ; Vol. 54, No. 1. pp. 31-44.

BibTeX

@article{4c6acf40a9ef4346b64f42175bc547b9,

title = "Constructing a Trapped Mode at Low Frequencies in an Elastic Waveguide",

abstract = "For any small ε > 0, a two-dimensional elastic waveguide is constructed such that λe = ε4 is the only eigenvalue in the vicinity of the lower bound λ† = 0 of the continuous spectrum. This result is rather unexpected, because an acoustic waveguide (the Neumann problem for the Laplace operator) with an arbitrary small localized perturbation cannot support a trapped mode at a low frequency.",

keywords = "continuous spectrum, orthotropic elastic waveguide, trapped waves at low frequencies",

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

note = "Nazarov, S.A. Constructing a Trapped Mode at Low Frequencies in an Elastic Waveguide. Funct Anal Its Appl 54, 31–44 (2020). https://doi.org/10.1134/S0016266320010049",

year = "2020",

month = jan,

doi = "10.1134/S0016266320010049",

language = "English",

volume = "54",

pages = "31--44",

journal = "Functional Analysis and its Applications",

issn = "0016-2663",

publisher = "Springer Nature",

number = "1",

}

RIS

TY - JOUR

T1 - Constructing a Trapped Mode at Low Frequencies in an Elastic Waveguide

AU - Nazarov, S. A.

N1 - Nazarov, S.A. Constructing a Trapped Mode at Low Frequencies in an Elastic Waveguide. Funct Anal Its Appl 54, 31–44 (2020). https://doi.org/10.1134/S0016266320010049

PY - 2020/1

Y1 - 2020/1

N2 - For any small ε > 0, a two-dimensional elastic waveguide is constructed such that λe = ε4 is the only eigenvalue in the vicinity of the lower bound λ† = 0 of the continuous spectrum. This result is rather unexpected, because an acoustic waveguide (the Neumann problem for the Laplace operator) with an arbitrary small localized perturbation cannot support a trapped mode at a low frequency.

AB - For any small ε > 0, a two-dimensional elastic waveguide is constructed such that λe = ε4 is the only eigenvalue in the vicinity of the lower bound λ† = 0 of the continuous spectrum. This result is rather unexpected, because an acoustic waveguide (the Neumann problem for the Laplace operator) with an arbitrary small localized perturbation cannot support a trapped mode at a low frequency.

KW - continuous spectrum

KW - orthotropic elastic waveguide

KW - trapped waves at low frequencies

UR - http://www.scopus.com/inward/record.url?scp=85090049523&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/e75e5aee-fde5-39f4-a1a7-2ab64e709f58/

U2 - 10.1134/S0016266320010049

DO - 10.1134/S0016266320010049

M3 - Article

AN - SCOPUS:85090049523

VL - 54

SP - 31

EP - 44

JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

SN - 0016-2663

IS - 1

ER -

ID: 62107745