Boundless Metamaterial Experimentation: Physical Realization of a Unidirectional Virtual Periodic Boundary Condition

Abstract

We experimentally implement a one-directional virtual geometric periodicity in an elastic metamaterial. First, unwanted boundary reflections at the domain ends are cancelled through the iterative injection of the polarity-reversed reflected wave field. The resulting boundless experimental state allows for a much better analysis of the influence of metamaterials on the propagating wave field. Subsequently, the propagating wave field exiting on one end of the structure is reintroduced at the opposite end, creating a virtual geometric periodicity in one propagation direction. We find that the experimentally observed band gap converges to the analytical solution through the introduction of the virtual periodicity. The established work flow introduces an approach to the experimental investigation and validation of metamaterial prototypes in the presence of strongly dispersive wave propagation and internal scattering. The fully data-driven ad hoc treatment of boundary conditions in metamaterial experimentation with arbitrary mechanical properties enables reflection suppression, virtual periodicity, and the introduction of more general fictitious boundaries.