TY - JOUR

T1 - Scattering of Low-Frequency Elastic Waves in An Infinite Kirchhoff Plate

AU - Nazarov, S. A.

N1 - Nazarov, S.A. Scattering of Low-Frequency Elastic Waves in An Infinite Kirchhoff Plate. J Math Sci 252, 664–686 (2021). https://doi.org/10.1007/s10958-021-05189-6

PY - 2021/2

Y1 - 2021/2

N2 - For a small frequency, scattering of waves propagating along a Kirchhoff plate in the shape of locally perturbed strip with traction-free edges is studied. An asymptotic analysis shows that both, bending and twisting, waves do not in main detect distortion of the originally straight edges, that is the transmission coefficient differs a little from 1 while other scattering coefficients become small. In other words, an effect similar to the Weinstein anomalies in an acoustic waveguide is observed. Asymptotic procedures are based on a detailed investigation of the spectrum of an auxiliary operator pencil and the corresponding stationary problem. Justification of the derived asymptotic expansions is performed by means of the technique of weighted spaces with detached asymptotics.

AB - For a small frequency, scattering of waves propagating along a Kirchhoff plate in the shape of locally perturbed strip with traction-free edges is studied. An asymptotic analysis shows that both, bending and twisting, waves do not in main detect distortion of the originally straight edges, that is the transmission coefficient differs a little from 1 while other scattering coefficients become small. In other words, an effect similar to the Weinstein anomalies in an acoustic waveguide is observed. Asymptotic procedures are based on a detailed investigation of the spectrum of an auxiliary operator pencil and the corresponding stationary problem. Justification of the derived asymptotic expansions is performed by means of the technique of weighted spaces with detached asymptotics.

UR - http://www.scopus.com/inward/record.url?scp=85099050792&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/4e749841-9c86-309b-9bac-d94e8e72e56a/

U2 - 10.1007/s10958-021-05189-6

DO - 10.1007/s10958-021-05189-6

M3 - Article

AN - SCOPUS:85099050792

VL - 252

SP - 664

EP - 686

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -