Special Soft Matter Seminar

Abstract

Periodic networks on the verge of mechanical instability, called Maxwell lattices, are known to exhibit zero-frequency modes localized to their boundary. Importantly, these zero modes are protected against disorder by their reciprocal-space topology so that the edge-selectivity is referred to as the topological polarization of the lattice. Here, we investigate a class of mechanical bilayers as a model system for designing topologically protected edge modes that couple in-plane extensional modes to out-of-plane flexural modes, a paradigm that we refer to as omnimodal polarization. We develop a design principle that utilizes mirror-symmetric kagome bilayers, which inherit the topological polarization of their constitutive planar monolayers. The coupling between these layers results in the omnimodal polarization of the bilayer, whereby extensional and flexural edge modes localize on the same edge, by antisymmetric actuation of the in-plane edge modes. We expand upon these theoretical results by fabricating a mirror-symmetric kagome bilayer with elastic beams via additive manufacturing. We show that the frequency of the edge modes scale with the bending stiffness of the beams until they hybridize with the bulk modes and delocalize. Finally, we confirm this simultaneous edge- and frequency-selectivity via finite element analysis and laser-vibrometry experiments.