Feedback-based Topological Mechanical Metamaterials

We present a method to design autonomous active metamaterials that can create arbitrary physical interactions on a single, reprogrammable platform, including non-local, non-linear, time-dependent or non-Newtonian couplings. The underlying principle includes application of external forces to a regular mechanical lattice, and processing them in real-time through closed-loop controllers that are pre-programmed to create desired couplings between the metamaterial sites. As an example, we demonstrate that a lattice constrained to out-of-plane vibration can be programmed to exhibit an analogy either of the quantum spin Hall effect, or the quantum Hall effect, thereby enabling a versatile unconventional guiding of mechanical waves.