Blockage, trapping and waveguide modes for flexural waves in a semi-infinite double grating

TL;DR

This paper investigates how flexural waves in Kirchhoff plates interact with semi-infinite double gratings, introducing new analytical and approximation methods to understand wave blocking, trapping, and waveguide modes.

Contribution

It introduces a novel analysis of flexural wave scattering using a quasi-periodic Green's function and an effective waveguide approximation for semi-infinite gratings.

Findings

Comparison of Green's function and effective waveguide methods

Analytical solution for finite truncated system

Insights into wave blocking and trapping phenomena

Abstract

The paper presents a novel view on the scattering of a flexural wave in a Kirchhoff plate by a semi-infinite discrete system. Blocking and channelling of flexural waves are of special interest. A quasi-periodic two-source Green's function is used in the analysis of the waveguide modes. An additional "effective waveguide" approximation has been constructed. Comparisons are presented for these two methods in addition to an analytical solution for a finite truncated system.