Bandgap formation and chaos in periodic lattices with graded bistable resonators

The interest for the study of metamaterials and metastructures has been rapidly increasing in the scientific community. A number of different approaches for the configuration of such systems have already shown to produce unique and potentially useful dynamic behavior, such as broadband vibration attenuation and negative mechanical properties. Locally resonant metamaterials are of special interest in this domain because of its versatility in creating wide bandgaps for wave propagation while being relatively simple in terms of analysis and experimental reproduction. Two specific subcategories of this type of systems have shown to enable specially promising bandgap formation behavior: nonlinear resonators and functionally graded, or rainbow, metamaterials. This work presents the yet unexplored combination of these two characteristics, showing that graded bistable nonlinear resonators can further widen the broadband vibration attenuation for a simple 1-D periodic lattice system due to chaotic response. This work also presents an contribution on the phenomenology of the vibration attenuation mechanisms with chaotic behavior.