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

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 t...

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Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2021-02, Vol.252 (5), p.664-686
Main Author: Nazarov, S. A.
Format: Article
Language:English
Subjects:
Acoustic waveguides
Anomalies
Asymptotic methods
Asymptotic series
Elastic scattering
Elastic waves
Mathematics
Mathematics and Statistics
Scattering coefficient
Twisting
Wave propagation
Waveguides
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description 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.
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subjects Acoustic waveguides
Anomalies
Asymptotic methods
Asymptotic series
Elastic scattering
Elastic waves
Mathematics
Mathematics and Statistics
Scattering coefficient
Twisting
Wave propagation
Waveguides
title Scattering of Low-Frequency Elastic Waves in An Infinite Kirchhoff Plate
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