In this Letter, we introduce a paradigm to realize magnetomechanical metastructures inspired by multilayer two-dimensional materials, such as graphene bilayers. The metastructures are intended to capture two aspects of their nanoscale counterparts. One is the multilayer geometry, which is implemented by stacking hexagonal lattice sheets. The other is the landscape of weak interlayer forces, which is mimicked by the interactions between pairs of magnets located at corresponding lattice sites on adjacent layers. We illustrate the potential of this paradigm through a three-layer prototype. The two rigid outer lattices serve as control layers, while the thin inner layer is free to experience flexural motion under the confining action of the magnetic forces exchanged with the outer ones, thus behaving as a lattice on an elastic foundation. The inner layer is free to rotate relative to the others, giving rise to a rich spectrum of interlayer interaction patterns. Our objective is to determine how the dynamical response can be tuned by changing the twist angle between the layers. Specifically, we demonstrate experimentally that switching between different stacking patterns has profound consequences on the phonon landscape, opening and closing band gaps in different frequency regimes.

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• Graphene
• Honeycomb lattice
• Bloch wave theory
• Finite-element method