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arXiv · 2310.00182

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

Tamanna Akter Jui·Raj Kumar Pal
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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.

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Tamanna Akter Jui, Raj Kumar Pal. 2023-09-29. Topological Localized Modes In Moir\'{e} Lattices of Bilayer Elastic Plates With Resonators. https://arxiv.org/abs/2310.00182

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