Nonlinear energy localisation in a model of plane metamaterial

Abstract

Applying the concepts of nonlinear normal modes and limiting phase trajectories introduced by Manevitch in Manevitch (Arch Appl Mech 77:301–312, 2007) to a two-dimensional mass–spring system, the authors propose a generalised method to tune a plane metamaterial and get the desirable resonant behaviour at short wavelengths. Indeed, the account of nonlinear coupling between the oscillators enables the localisation of energy leading the origin of a bandgap at short wavelengths regardless the existence of external disturbances. Moreover, further restrictions on the modes amplitude allow the observation of Fermi–Pasta–Ulam–Tsingou recurrence and super-recurrence in the two-dimensional metamaterial. These findings can open the way to further research in order to improve efficiency and performance of resonant metamaterials.