No abstract

This study introduces a novel framework for local resonant systems to low bandgap frequencies without greatly increasing spatial penalties in grid structures. The proposed double-spiral resonator (DSR) consists of a pair of spiral spring-like structures and a rigid plate acting as the “mass” of the oscillating system, which can serve as an effective mechanical filter. A rapid and accurate calculation based on the stiffness matrix method is proposed to precisely predict the fundamental resonant frequency of the resonator. Periodic installation of these resonators in a grid-like beam structure can lead to the formation of a new type of metastructure that possesses negative effective properties. Investigations on the bandgap characteristics of the proposed metastructure are conducted using the finite element method. It is found that a low-frequency resonant-type bandgap is present in such a structure. Changing the thickness of the central mass or the number of parasitic beam segments enables the manipulation of the bandgap location. The validity of the analytical results is evaluated via comparison with the finite element results and experimental measurements. By using multiple resonators with similar resonance frequencies, the attenuation bandwidth can be effectively broadened. The physics behind wave attenuation can be realized by introducing a negative effective mass density. The results demonstrate that the proposed structure exhibiting unique dynamic characteristics can successfully attenuate undesired structural vibrations at low frequencies. It may be concluded that this DSR can be used as an alternative to current vibration filtering systems.