Topological localized modes in moiré lattices of bilayer elastic plates with resonators

Abstract

We investigate the existence of higher order topological localized modes in moiré lattices of bilayer elastic plates. Each plate has a hexagonal array of discrete resonators and one of the plates is rotated at an angle (21.78∘) which results in a periodic moiré 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 moiré structures opens opportunities for novel wave phenomena, with potential applications in tunable energy localization and vibration isolation.