Trapping of Waves in Semiinfinite Kirchhoff Plate with Periodically Damaged Edge

Standard

Trapping of Waves in Semiinfinite Kirchhoff Plate with Periodically Damaged Edge. / Nazarov, S. A.

In: Journal of Mathematical Sciences (United States), Vol. 257, No. 5, 09.2021, p. 684-704.

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

Author

Nazarov, S. A. / Trapping of Waves in Semiinfinite Kirchhoff Plate with Periodically Damaged Edge. In: Journal of Mathematical Sciences (United States). 2021 ; Vol. 257, No. 5. pp. 684-704.

BibTeX

@article{bdb6b139ea6c46f298008571673a701b,

title = "Trapping of Waves in Semiinfinite Kirchhoff Plate with Periodically Damaged Edge",

abstract = "We study analogues of the Rayleigh waves in a semiinfinite Kirchhoff plate with periodic edges (the Neumann problem for the biharmonic operator) and in an infinite plate with a periodic family of foreign inclusions. In the first case, we prove the existence of localized waves (exponentially decaying in the perpendicular direction) for any edge profile. In the second case, we obtain a sufficient condition for trapping of waves. We explain why the results obtained for the biharmonic operator are different from the known results for the Helmholtz equation. In the case of threshold resonance, we construct asymptotic expansions of eigenvalues of the model problem, which generate analogues of the Stoneley waves. For a plate with a periodic family of cracks perpendicular to the straight boundary of the half-plane, we detect periodic localized Floquet waves that do not transfer energy.",

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

note = "Nazarov, S.A. Trapping of Waves in Semiinfinite Kirchhoff Plate with Periodically Damaged Edge. J Math Sci 257, 684–704 (2021). https://doi.org/10.1007/s10958-021-05510-3",

year = "2021",

month = sep,

doi = "10.1007/s10958-021-05510-3",

language = "English",

volume = "257",

pages = "684--704",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "5",

}

RIS

TY - JOUR

T1 - Trapping of Waves in Semiinfinite Kirchhoff Plate with Periodically Damaged Edge

AU - Nazarov, S. A.

N1 - Nazarov, S.A. Trapping of Waves in Semiinfinite Kirchhoff Plate with Periodically Damaged Edge. J Math Sci 257, 684–704 (2021). https://doi.org/10.1007/s10958-021-05510-3

PY - 2021/9

Y1 - 2021/9

N2 - We study analogues of the Rayleigh waves in a semiinfinite Kirchhoff plate with periodic edges (the Neumann problem for the biharmonic operator) and in an infinite plate with a periodic family of foreign inclusions. In the first case, we prove the existence of localized waves (exponentially decaying in the perpendicular direction) for any edge profile. In the second case, we obtain a sufficient condition for trapping of waves. We explain why the results obtained for the biharmonic operator are different from the known results for the Helmholtz equation. In the case of threshold resonance, we construct asymptotic expansions of eigenvalues of the model problem, which generate analogues of the Stoneley waves. For a plate with a periodic family of cracks perpendicular to the straight boundary of the half-plane, we detect periodic localized Floquet waves that do not transfer energy.

AB - We study analogues of the Rayleigh waves in a semiinfinite Kirchhoff plate with periodic edges (the Neumann problem for the biharmonic operator) and in an infinite plate with a periodic family of foreign inclusions. In the first case, we prove the existence of localized waves (exponentially decaying in the perpendicular direction) for any edge profile. In the second case, we obtain a sufficient condition for trapping of waves. We explain why the results obtained for the biharmonic operator are different from the known results for the Helmholtz equation. In the case of threshold resonance, we construct asymptotic expansions of eigenvalues of the model problem, which generate analogues of the Stoneley waves. For a plate with a periodic family of cracks perpendicular to the straight boundary of the half-plane, we detect periodic localized Floquet waves that do not transfer energy.

UR - http://www.scopus.com/inward/record.url?scp=85113906181&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/3a184e64-b12a-31e9-976e-a1987a8c67e1/

U2 - 10.1007/s10958-021-05510-3

DO - 10.1007/s10958-021-05510-3

M3 - Article

AN - SCOPUS:85113906181

VL - 257

SP - 684

EP - 704

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -

ID: 88365641