Omnimodal topological polarization of bilayer networks: analysis in the Maxwell limit and experiments on a 3D-printed prototype

TL;DR

This paper introduces a new class of bilayer mechanical networks exhibiting topologically protected edge modes that couple in-plane and out-of-plane vibrations, demonstrated through theoretical analysis and experimental validation with 3D-printed prototypes.

Contribution

It presents the concept of omnimodal polarization in bilayer Maxwell lattices and provides an analytical method to predict topological polarization in mirror-symmetric bilayers.

Findings

Identification of mirror-symmetric bilayers with analytically predictable polarization

Coupling of in-plane and out-of-plane edge modes on the same boundary

Experimental confirmation using 3D-printed kagome bilayer network

Abstract

Periodic networks on the verge of mechanical instability, called Maxwell lattices, are known to exhibit zero-frequency modes localized to their boundaries. Topologically polarized Maxwell lattices, in particular, focus these zero modes to one of their boundaries in a manner that is protected against disorder by the reciprocal-space topology of the lattice's band structure. Here, we introduce a class of mechanical bilayers as a model system for designing topologically protected edge modes that couple in-plane dilational and shearing modes to out-of-plane flexural modes, a paradigm that we refer to as omnimodal polarization. While these structures exhibit a high-dimensional design space that makes it difficult to predict the topological polarization of generic geometries, we are able to identify a family of mirror-symmetric bilayers that inherit the in-plane modal localization of their constitutive monolayers whose topological polarization can be determined analytically. Importantly, the coupling between the layers results in the emergence of omnimodal polarization, whereby in-plane and out-of-plane edge modes localize on the same edge. We demonstrate these theoretical results by fabricating a mirror-symmetric, topologically polarized kagome bilayer consisting of a network of elastic beams via additive manufacturing and confirm this finite-frequency polarization via finite element analysis and laser-vibrometry experiments.