A robust optimised multi-material 3D inkjet printed elastic metamaterial

This paper presents and validates a novel elastic metamaterial design, that is optimised for broadband robust vibration control of a structure in the presence of uncertainties, and realised using multi-material additive manufacturing. A novel concept resonator design that allows the resonance frequency to be flexibly tuned via both geometrical and material property modifications is presented and characterised. A unit cell consisting of 12 of these resonators is then proposed. The resonance frequencies and damping ratios of this elastic metamaterial unit cell when attached to a parametrically uncertain example structure are then optimised using a Particle Swarm Optimisation to maximise the mean attenuation in kinetic energy of a structure with parametric uncertainties, based on an analytical model of the system. The performance of the optimised metamaterial is then validated experimentally, and it is shown that the realised metamaterial design is able to achieve a mean of 3.5 dB of broadband attenuation in the presence of uncertainties in the structure. In addition, in the presence of structural uncertainties the robustly optimised design achieves 0.5 dB greater mean attenuation than a design optimised on the nominal structural response alone, and reduced variation in attenuation for different levels of uncertainty.