Optimization of connection architectures and mass distributions for metamaterials with multiple resonators

Metamaterials with multiple resonators have been widely investigated for the purpose of generating multiple stop bands or broadening the attenuation bandwidth. The multiple resonators could be connected end to end in a line, namely, in-series connection, or connected individually to the host structures, namely, in-parallel connection. This paper investigates the influence of the resonator connection methodology on the frequency response functions of metamaterial beams with multiple resonators and exhibits an approach for optimizing their resonator distribution over the structure. The receptance functions of metamaterial beams with various resonator connection architectures are calculated by a transfer matrix model, which is verified through finite element model results. It is demonstrated that resonator interconnection architectures have a great impact on the global dynamic properties of metamaterials. An optimization strategy is subsequently proposed to find out the optimal resonator connection architectures and mass distributions that could minimize the maximal receptance functions in targeted single and multiple frequency ranges. The objective functions within single targeted frequency ranges are solved by the adoption of the genetic algorithm method. The weighted sum method is used to gain an optimal solution for multi-frequency range optimization. The metamaterial beams with optimal resonator connection methods and mass distributions demonstrate greatly enhanced vibration attenuation at frequencies of interest compared with other beams. The work is expected to provide the necessary theoretical basis and incentive for future researchers working on the design of metamaterials with extended, tuned, and optimized stop bands.