Boundless metamaterial experimentation: physical realization of a virtual periodic boundary condition

Abstract

We experimentally implement a 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 wavefield. The resulting boundless experimental state allows for a much better analysis of the metamaterials influence on the propagating wavefield. Subsequently, the propagating wavefield exiting on one end of the structure is reintroduced at the opposite end, creating a virtual geometric periodicity. We find that the experimentally observed band gap converges to the analytical solution through the introduction of the virtual periodicity. The established workflow introduces a novel 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. I. INTRODUCTIONEngineered metamaterials have long since proven their capabilities to exhibit extraordinary material properties [1-3], as well as manipulate and attenuate wave propagation [4,5] using band gaps. Such prohibited frequency ranges can be architected into materials via either Bragg scattering phononic crystals [6] or locally resonant metamaterials [7]. The later enables sub-wavelenghth bandgaps [8] and has recently been leveraged for broadband energy harvesting [9][10][11][12]. Numerical simulations drive the development of metamaterials, the ever increasing available computational power making it feasible to rapidly model different designs. Nevertheless, experimental investigation and validation of prototype structures remains essential. Whereas in numerical studies, effects such as low absorbing boundary layers or local damping [13,14] can be introduced to simulate free space wave propagation, laboratory experiments are often plagued by modal responses of the system caused by, e.g., free or clamped boundaries. Additionally, wave propagation within the structure is difficult to interpret due to boundary reflections. Thus, it is often challenging to accurately distinguish phenomena caused by the metamaterial under study from those of the whole system. Con- *