Edge modes for flexural waves in quasi-periodic linear arrays of scatterers

TL;DR

This paper investigates topologically protected interface modes for flexural waves in quasi-periodic scatterer arrays on elastic plates, demonstrating their robustness against disorder and potential for wave manipulation.

Contribution

It introduces a multiple scattering analysis revealing robust, topologically inspired interface states in quasi-periodic arrays supporting flexural waves, with implications for wave control.

Findings

Modes form a Hofstadter butterfly spectrum.

Interface states are robust against disorder.

Modes are suitable for excitation by propagating waves.

Abstract

We present a multiple scattering analysis of robust interface states for flexural waves in thin elastic plates. We show that finite clusters of linear arrays of scatterers built on a quasi-periodic arrangement support bounded modes in the two-dimensional space of the plate. The spectrum of these modes plotted against the modulation defining the quasi-periodicity has the shape of a Hofstadter butterfly, which previous works suggest that might support topologically protected modes. Some interface states appear inside the gaps of the butterfly, which are enhanced when one linear cluster is merged with its mirror reflected version. The robustness of these modes is verified by numerical experiments in which different degrees of disorder are introduced in the scatterers, showing that neither the frequency nor the shape of the modes is altered. Since the modes are at the interface between two one-dimensional arrays of scatterers deposited on a two-dimensional space, these modes are not fully surrounded by bulk gaped materials, so that they are more suitable for their excitation by propagating waves. The generality of these results goes beyond flexural waves, since similar results are expected for acoustic or electromagnetic waves.