Study on the low-frequency bandgap characteristics of the microsphere array three-dimensional phononic crystal

A three-dimensional, microsphere array, locally resonant phononic crystal has been designed to address the problem of low-frequency vibration in the range of 50-350 Hz in engineering applications. The energy band and transmission loss are calculated using the finite element method. The bandgap formation mechanism is analyzed by co-constructing the mass-spring model and displacement mode. In addition, the effects of material composition, geometric parameters, asymmetry of the connections, and the coating layer containing periodic holes on the bandgap are studied. The results show that as the diameter of the connections decreased, the aperture of the coating layer reduced, and the asymmetry of the connections enhanced, the bandgap of the three-component phononic crystal broadened. When the diameter of the connections is 1 mm, this work achieves the widest mid-gap ratio of 182.76%. Compared to existing models, it has a wider mid-gap ratio. The research results reveal the suppression mechanism and quantify the effectiveness of the proposed metastructure, thereby providing a concrete strategy for attenuating elastic wave propagation within the 50-350 Hz range.