Embedding 1D topological models into elastic plates through local resonances

Topological metamaterials have opened new avenues to control waves and vibrations across various domains, including elastic and acoustic systems. In this study, we focus on 1D elastic topological metamaterials of the BDI class and describe a design principle to embed them in continuous elastic plates. The design relies on tailoring the coupling of local resonances in a plate. Starting with a plate having a periodic arrangement of square pillars, which allows establishing a bulk bandgap, some pillars are selectively removed along one dimension. These intentionally introduced line defects support local resonances within the bandgap and effectively form a chain of coupled resonators. The coupling strength is tuned by adjusting the height and shape of the intermediate pillars. The precise control of the coupling scheme can reproduce chiral symmetry, so far an elusive property to obtain in continuous elastic systems. The design principle is closely related to 1D tight-binding models, that is, defects act as “atoms” (or resonators) while the intermediate pillars control their interaction strength.

Numerical results are presented to show that this approach can generate elastic analogs of the canonical Su-Schrieffer-Heeger (SSH) model and of the dual SSH model, which to-date have not been reproduced in fully continuous elastic systems. The topological character of the resulting waveguides is verified by computing the winding number invariant and by showing the occurrence of edge modes within the bulk bandgap.