Standard

The Discrete Spectrum of an Infinite Kirchhoff Plate in the Form of a Locally Perturbed Strip. / Bakharev, F. L.; Nazarov, S. A.

In: Siberian Mathematical Journal, Vol. 61, No. 2, 01.03.2020, p. 233-247.

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

Harvard

Bakharev, FL & Nazarov, SA 2020, 'The Discrete Spectrum of an Infinite Kirchhoff Plate in the Form of a Locally Perturbed Strip', Siberian Mathematical Journal, vol. 61, no. 2, pp. 233-247. https://doi.org/10.1134/S0037446620020056

APA

Bakharev, F. L., & Nazarov, S. A. (2020). The Discrete Spectrum of an Infinite Kirchhoff Plate in the Form of a Locally Perturbed Strip. Siberian Mathematical Journal, 61(2), 233-247. https://doi.org/10.1134/S0037446620020056

Vancouver

Bakharev FL, Nazarov SA. The Discrete Spectrum of an Infinite Kirchhoff Plate in the Form of a Locally Perturbed Strip. Siberian Mathematical Journal. 2020 Mar 1;61(2):233-247. https://doi.org/10.1134/S0037446620020056

Author

Bakharev, F. L. ; Nazarov, S. A. / The Discrete Spectrum of an Infinite Kirchhoff Plate in the Form of a Locally Perturbed Strip. In: Siberian Mathematical Journal. 2020 ; Vol. 61, No. 2. pp. 233-247.

BibTeX

@article{a40b7cbf6c4c405d85a31fe47bc18814,
title = "The Discrete Spectrum of an Infinite Kirchhoff Plate in the Form of a Locally Perturbed Strip",
abstract = "We study the discrete spectra of boundary value problems for the biharmonic operator describing oscillations of a Kirchhoff plate in the form of a locally perturbed strip with rigidly clamped or simply supported edges. The two methods are applied: variational and asymptotic. The first method shows that for a narrowing plate the discrete spectrum is empty in both cases, whereas for a widening plate at least one eigenvalue appears below the continuous spectrum cutoff for rigidly clamped edges. The presence of the discrete spectrum remains an open question for simply supported edges. The asymptotic method works only for small variations of the boundary. While for a small smooth perturbation the construction of asymptotics is generally the same for both types of boundary conditions, the asymptotic formulas for eigenvalues can differ substantially even in the main correction term for a perturbation with corner points.",
keywords = "biharmonic operator, discrete spectrum, eigenvalue asymptotics, infinite Kirchhoff plate",
author = "Bakharev, {F. L.} and Nazarov, {S. A.}",
year = "2020",
month = mar,
day = "1",
doi = "10.1134/S0037446620020056",
language = "English",
volume = "61",
pages = "233--247",
journal = "Siberian Mathematical Journal",
issn = "0037-4466",
publisher = "Springer Nature",
number = "2",

}

RIS

TY - JOUR

T1 - The Discrete Spectrum of an Infinite Kirchhoff Plate in the Form of a Locally Perturbed Strip

AU - Bakharev, F. L.

AU - Nazarov, S. A.

PY - 2020/3/1

Y1 - 2020/3/1

N2 - We study the discrete spectra of boundary value problems for the biharmonic operator describing oscillations of a Kirchhoff plate in the form of a locally perturbed strip with rigidly clamped or simply supported edges. The two methods are applied: variational and asymptotic. The first method shows that for a narrowing plate the discrete spectrum is empty in both cases, whereas for a widening plate at least one eigenvalue appears below the continuous spectrum cutoff for rigidly clamped edges. The presence of the discrete spectrum remains an open question for simply supported edges. The asymptotic method works only for small variations of the boundary. While for a small smooth perturbation the construction of asymptotics is generally the same for both types of boundary conditions, the asymptotic formulas for eigenvalues can differ substantially even in the main correction term for a perturbation with corner points.

AB - We study the discrete spectra of boundary value problems for the biharmonic operator describing oscillations of a Kirchhoff plate in the form of a locally perturbed strip with rigidly clamped or simply supported edges. The two methods are applied: variational and asymptotic. The first method shows that for a narrowing plate the discrete spectrum is empty in both cases, whereas for a widening plate at least one eigenvalue appears below the continuous spectrum cutoff for rigidly clamped edges. The presence of the discrete spectrum remains an open question for simply supported edges. The asymptotic method works only for small variations of the boundary. While for a small smooth perturbation the construction of asymptotics is generally the same for both types of boundary conditions, the asymptotic formulas for eigenvalues can differ substantially even in the main correction term for a perturbation with corner points.

KW - biharmonic operator

KW - discrete spectrum

KW - eigenvalue asymptotics

KW - infinite Kirchhoff plate

UR - http://www.scopus.com/inward/record.url?scp=85086336437&partnerID=8YFLogxK

U2 - 10.1134/S0037446620020056

DO - 10.1134/S0037446620020056

M3 - Article

AN - SCOPUS:85086336437

VL - 61

SP - 233

EP - 247

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 2

ER -

ID: 60873342