Rainbow metamaterials for broadband multi-frequency vibration attenuation: Numerical analysis and experimental validation

In this study, we propose a ‘rainbow’ metamaterial to achieve broadband multi-frequency vibration attenuation. The rainbow metamaterial is constituted of a Π-shaped beam partitioned into substructures by parallel plates insertions with two attached cantilever-mass acting as local resonators. Both resonators inside each substructure can be non-symmetric such that the metamaterial can have multi-frequency bandgaps. Furthermore, these cantilever-mass resonators have a progressively variant design along the beam, namely rainbow-shaped, for the purpose of achieving broader energy stop bands. Π-shaped beams partitioned by parallel plate insertions can be extended to honeycomb sandwich composites, hence the proposed rainbow metamaterial can serve as a precursor for future honeycomb composites with superior vibration attenuation for more industrial applications. A mathematical model is first developed to estimate the frequency response functions of the metamaterial. Interaction forces between resonators and the backbone structure are calculated by solving the displacement of the cantilever-mass resonators. The plate insertions are modeled as attached masses with both their translational and rotational motion considered. Subsequently, the mathematical model is verified by comparison with experimental results. Metamaterials fabricated through an additive manufacturing technique are tested with a laser doppler receptance measuring system. After the validation of the mathematical model, a numerical study is conducted to explore the influences of the resonator spatial distributions on the frequency response functions of structures. Results show that for metamaterials with both symmetric and non-symmetric resonators, rainbow-shaped resonators can introduce inertial forces inside wider frequency range when compared to the periodic resonators of the same total mass, hence broader bandgaps. Meanwhile, the attenuation inside the bandgaps decreases when the bandgap become broader. Metamaterials with broadband multi-frequency range vibration attenuation can be achieved with non-symmetric sinusoidally varying resonators