A frequency response function-based optimization for metamaterial beams considering both location and mass distributions of local resonators

To date, phononic crystals/metamaterials normally adopt classical periodic configurations, and optimization strategies for them are based primarily on dispersion relations from a repeated unit cell. In this study, a frequency response function (FRF) based optimization scheme is presented for a locally resonant metamaterial beam that considers both the resonant frequencies and distribution locations of the resonators. Three optimization objectives involving (1) broadband, (2) multi-band, and (3) high-attenuation characteristics are exploited as study cases, and a single-objective genetic algorithm is used to determine the optimal solutions for the prescribed bandgap targets. The spectral element method is used as an analytic formulation to determine the metamaterial FRFs, and the finite element method is used to validate the effectiveness of the optimization strategy. The results reveal that these objective bandgap characteristics can be enabled without increasing the resonator mass following the proposed optimization procedure. This shows the potential of adjusting the locations and resonance frequencies of resonators in metamaterial beams beyond the widely accepted periodic structures. The most important finding of this study is that promising bandgap properties can be easily realized with only single-degree-of-freedom resonators instead of designing more complex ones or multi-resonators. This FRF-based optimization method can be considered as a simple but instructive strategy for optimal or inverse designs in metamaterials.