Embedding 1D BDI topological dynamics into continuous elastic plates

Abstract

This study presents an approach that leverages the existing knowledge acquired in one-dimensional BDI class discrete metamaterials, such as mass-spring systems or acoustic resonators, and exploits it to realize fully continuous elastic two-dimensional topological waveguides. The design relies on the concept of evanescently coupled waveguides and defect resonances in order to reproduce the equivalent dynamics of prototypical BDI discrete systems, such as the Su-Schrieffer-Heeger (SSH) model. Starting with a continuous plate waveguide based on a periodic distribution of pillars, local resonators and waveguides are created by eliminating selected pillars and by exploiting the concept of point and line defects. The height of selected pillars is adjusted to tune the coupling strength between different resonators. The approach is validated by designing fully continuous elastic analogs of both the SSH chain and ladder systems. Numerical simulations and experimental results confirm the validity of the design by showing the emergence of topological edge modes at the interface of topologically distinct systems. In addition, the edge modes obtained in the elastic analog of the SSH ladder are shown to be Majorana-like modes.