Asymptotic Eigenmodes Localized Near the Edge of a Vessel, with Acoustic Medium, Which Is Covered by a Thin Elastic Membrane

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Asymptotic Eigenmodes Localized Near the Edge of a Vessel, with Acoustic Medium, Which Is Covered by a Thin Elastic Membrane. / Лялинов, Михаил Анатольевич.

In: Russian Journal of Mathematical Physics, Vol. 31, No. 3, 01.09.2024, p. 477–494.

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

BibTeX

@article{e18d39100d8442c8a3cd2ec7d3aa71c5,

title = "Asymptotic Eigenmodes Localized Near the Edge of a Vessel, with Acoustic Medium, Which Is Covered by a Thin Elastic Membrane",

abstract = "The paper deals with the formal short-wavelength asymptotic solutions describing theacoustic eigenoscillations in a vessel having a hard bottom, filled in by an acoustic medium, andcovered by a thin elastic membrane. The solutions are localized in the medium near the line of therigid contact of the membrane covering the vessel with the edge of the vessel. The coefficients in theasymptotic expansion of the solutions satisfy a recurrent sequence of solvable problems, whereas thefrequencies, for which such nontrivial formal solutions exist, obey an asymptotic {\textquoteleft}quantization-typecondition.",

author = "Лялинов, {Михаил Анатольевич}",

year = "2024",

month = sep,

day = "1",

doi = "10.1134/s1061920824030105",

language = "English",

volume = "31",

pages = "477–494",

journal = "Russian Journal of Mathematical Physics",

issn = "1061-9208",

publisher = "МАИК {"}Наука/Интерпериодика{"}",

number = "3",

}

RIS

TY - JOUR

T1 - Asymptotic Eigenmodes Localized Near the Edge of a Vessel, with Acoustic Medium, Which Is Covered by a Thin Elastic Membrane

AU - Лялинов, Михаил Анатольевич

PY - 2024/9/1

Y1 - 2024/9/1

N2 - The paper deals with the formal short-wavelength asymptotic solutions describing theacoustic eigenoscillations in a vessel having a hard bottom, filled in by an acoustic medium, andcovered by a thin elastic membrane. The solutions are localized in the medium near the line of therigid contact of the membrane covering the vessel with the edge of the vessel. The coefficients in theasymptotic expansion of the solutions satisfy a recurrent sequence of solvable problems, whereas thefrequencies, for which such nontrivial formal solutions exist, obey an asymptotic ‘quantization-typecondition.

AB - The paper deals with the formal short-wavelength asymptotic solutions describing theacoustic eigenoscillations in a vessel having a hard bottom, filled in by an acoustic medium, andcovered by a thin elastic membrane. The solutions are localized in the medium near the line of therigid contact of the membrane covering the vessel with the edge of the vessel. The coefficients in theasymptotic expansion of the solutions satisfy a recurrent sequence of solvable problems, whereas thefrequencies, for which such nontrivial formal solutions exist, obey an asymptotic ‘quantization-typecondition.

UR - https://www.mendeley.com/catalogue/20a25354-9433-32e4-99d1-cb1dc13af542/

U2 - 10.1134/s1061920824030105

DO - 10.1134/s1061920824030105

M3 - Article

VL - 31

SP - 477

EP - 494

JO - Russian Journal of Mathematical Physics

JF - Russian Journal of Mathematical Physics

SN - 1061-9208

IS - 3

ER -

ID: 125320918