Phononic and Topological Characteristics of Kagome Lattices in The Limit of Continuum Elasticity

Topological floppy edge phonon modes have been discovered in families of Kagome lattices. While rigorous theory has been developed to characterize these modes with ball-spring models, little has been studied with continuum elasticity. Here we elucidate the in-plane phononic characteristics of 2D regular and topological Kagome structures in the limit of continuum elasticity. The single-point connection between triangular plates are hereby replaced by continuous ligaments to mimic structures that can be fabricated via water-jet (or laser) cutting or printing techniques. Through a combination of finite element analyses and experimental wave reconstruction techniques with a 3D Scanning Laser Doppler Vibrometer, we provide a full map of phononic characteristics of these lattices and a mechanistic rationale to interpret the observed wave features. Specifically, we uncover the emergence of floppy edge modes in topological Kagome configurations, which localize the lattice deformation at domain boundaries at low frequency. Our results have implications for the design of acoustic metamaterials for wave control and smart sensing applications, and can provide general guidelines for the dynamic experimental characterization of architected materials.