Edge waves in plates with resonators: An elastic analogue of the quantum valley Hall effect

TL;DR

This paper demonstrates topologically protected edge waves in elastic plates with resonators, drawing parallels to quantum valley Hall effects, and shows their potential for robust waveguiding in engineering applications.

Contribution

It introduces a novel elastic plate design with resonators that supports topologically protected edge waves, bridging concepts from quantum physics to elastic structures.

Findings

Edge waves are supported at interfaces with different topological invariants.

Numerical simulations confirm edge wave propagation within bulk bandgaps.

The design framework enables robust waveguiding in elastic structures.

Abstract

We investigate elastic periodic structures characterized by topologically nontrivial bandgaps supporting backscattering suppressed edge waves. These edge waves are topologically protected and are obtained by breaking inversion symmetry within the unit cell. Examples for discrete one and two-dimensional lattices elucidate the concept and illustrate parallels with the quantum valley Hall effect. The concept is implemented on an elastic plate featuring an array of resonators arranged according to a hexagonal topology. The resulting continuous structures have non-trivial bandgaps supporting edge waves at the interface between two media having different topological invariants. The topological properties of the considered configurations are predicted by unit cell and finite strip dispersion analyses. Numerical simulations on finite structures demonstrate edge wave propagation for excitation at frequencies belonging to the bulk bandgaps. The considered plate configurations define a framework for the implementation of topological concepts on continuous elastic structures of potential engineering relevance.