Scattering of low-frequency waves in infinite Kirchhoff plate

S. A. Nazarov

Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 49, Tome 483 (2019), pp. 142-177

Résumé

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 detect in main distortion of the straight edges, that is the transmission coefficient differs a little from one while other scattering coefficients become small. In other words, an effect similar to the Weinstein anomaly 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 asymptotics is performed by means of the technique of weighted spaces with detached asymptotics.