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Trapping of Waves in Semiinfinite Kirchhoff Plate with Periodically Damaged Edge. / Nazarov, S. A.
в: Journal of Mathematical Sciences (United States), Том 257, № 5, 09.2021, стр. 684-704.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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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