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Motion control of droplets has generated much attention for its application to microfluidics, where precisely controlling small fluid volumes is an imperative requirement. Mechanical vibrations can induce controllable depinning and activation of a variety of drop-motion regimes. However, existing vibration-based strategies establish homogeneous rigid-body dynamics on the entire substrate, thus lacking any form of spatial heterogeneity and tuning. Addressing this limitation, elastic metamaterials provide an ideal platform to achieve spectrally and spatially selective drop-motion control. This capability results from the intrinsic ability of metamaterials to attenuate vibrations in selected frequency bands and regions of an elastic domain. In this work, we experimentally demonstrate a variety of droplet motion capabilities on the surface of a vibrating metaplate endowed with locally resonant stubs. The experiments leverage the design reconfigurability of a LEGO^®component-enabled prototyping platform, which allows us to switch in an agile manner between different configurations of resonators. We use laser vibrometry measurements with high spatial resolution to capture the spatial variability of the metaplate response. Beyond the discipline-specific boundaries, this work begins to illustrate a broader employment of elastic metamaterials in applications where their signature wave control capability is not the end goal, but rather an enabling tool for other more complex multiphysical effects. 

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.