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.
|Original language||English (US)|
|Journal||Proceedings of the National Academy of Sciences of the United States of America|
|State||Published - Oct 4 2022|
Bibliographical noteFunding Information:
ACKNOWLEDGMENTS. This work was supported by NSF Grant EFRI-1741618 (to M.C. and S.G.) and the Office of Naval Research Multidisciplinary University Research Initiative N00014-20-1-2479 (to J.M., K.S., and X.M.) and leveraged the High Performance Computing systems at the Minnesota Supercomputing Institute.
Copyright © 2022 the Author(s). Published by PNAS.
- flexural modes
- mechanical metamaterials
- topological mechanics
PubMed: MeSH publication types
- Journal Article
- Research Support, U.S. Gov't, Non-P.H.S.