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Periodic networks on the verge of mechanical instability, called Maxwelllattices, are known to exhibit zero-frequency modes localized to theirboundaries. Topologically polarized Maxwell lattices, in particular, focusthese zero modes to one of their boundaries in a manner that is protectedagainst disorder by the reciprocal-space topology of the lattice's bandstructure. Here, we introduce a class of mechanical bilayers as a model systemfor designing topologically protected edge modes that couple in-planedilational and shearing modes to out-of-plane flexural modes, a paradigm thatwe refer to as omnimodal polarization. While these structures exhibit ahigh-dimensional design space that makes it difficult to predict thetopological polarization of generic geometries, we are able to identify afamily of mirror-symmetric bilayers that inherit the in-plane modallocalization of their constitutive monolayers whose topological polarizationcan be determined analytically. Importantly, the coupling between the layersresults in the emergence of omnimodal polarization, whereby in-plane andout-of-plane edge modes localize on the same edge. We demonstrate thesetheoretical results by fabricating a mirror-symmetric, topologically polarizedkagome bilayer consisting of a network of elastic beams via additivemanufacturing and confirm this finite-frequency polarization via finite elementanalysis and laser-vibrometry experiments.

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