Topological Localized Modes In Moir\'{e} Lattices of Bilayer Elastic Plates With Resonators

TL;DR

This paper explores higher order topological localized modes in moiré lattices of bilayer elastic plates with resonators, revealing corner modes and potential for tunable energy localization.

Contribution

It introduces a novel analysis of topological corner modes in elastic moiré lattices, combining dispersion analysis and numerical simulations to predict localized vibrations.

Findings

Bandgap opens with inter-layer springs

Corner localized modes are observed in finite structures

Topological index predicts corner mode presence

Abstract

We investigate the existence of higher order topological localized modes in moir\'{e} lattices of bilayer elastic plates. Each plate has a hexagonal array of discrete resonators and one of the plates is rotated an angle ($21.78^\circ$) which results in a periodic moir\'{e} lattice with the smallest area. The two plates are then coupled by inter-layer springs at discrete locations where the top and bottom plate resonators coincide. Dispersion analysis using the plane wave expansion method reveals that a bandgap opens on adding the inter-layer springs. The corresponding topological index, namely fractional corner mode, for bands below the bandgap predicts the presence of corner localized modes in a finite structure. Numerical simulations of frequency response show localization at all corners, consistent with the theoretical predictions. The considered continuous elastic bilayered moir\'{e} structures opens opportunities for novel wave phenomena, with potential applications in tunable energy localization and vibration isolation.