Dynamic properties of metamaterials with different resonator connection methods

This paper investigates the influences of resonator connection methods on the dynamic properties of the elastic metamaterials. A large number of metamaterials with multiple resonators were developed for the purpose of generating multiple bandgaps or broadening the bandwidth. The multiple resonators in a unit cell could be connected end to end in a line, i.e. in series connection, or connected individually to the substrate, i.e. in parallel connection. Resonator connection methods caused considerable differences to the dynamic properties of the metamaterials, it would hence be meaningful to investigate in depth the influences of connection methods, which could offer theoretical basis and foundation for the design of metamaterials with multiple resonators. An analytical model is first employed to calculate the dynamic properties of metamaterial beams with periodical single/in-series/in-parallel resonators respectively. After that, comparisons are made among the calculated frequency response functions of metamaterial beams with resonators of the same mass but different connections methods. It is found that in-series resonators lead to lower frequency bandgaps, while in-parallel resonators result in bandgaps with enlarged bandwidth compared with single resonators. An optimization strategy is also developed to search for the optimal resonator connection architectures and mass distributions that could minimize the maximal receptance functions in targeted frequency ranges. The metamaterial beams with optimal resonator connection methods and mass distributions demonstrate greatly enhanced vibration attenuation at frequencies of interest compared with other beams.