Comparative analysis of bandgap characteristics of single-and double-layer ring-like multi-oscillator locally resonant phononic crystals

Phononic crystals (PCs) harbor the potential to be applied to low-frequency elastic vibration wave control for its intrinsic bandgap property, but the development of conventional single-oscillator locally resonant phononic crystals (SOLRPCs) in the field of low-frequency vibration modulation is restricted by the narrow range of the bandgap. To this end, in this study, single- and double-layer ring-like multi-oscillator locally resonant phononic crystals (referred to as SL-RMLRPCs and DL-RMLRPCs) are constructed to broaden the overall characteristics of the bandgap at the level of the number and width of bandgap. The bandgap characteristic is determined by calculating the energy band structure based on the finite element method, and the intrinsic formation mechanism of the bandgap is investigated with vibrational modal analysis. On this basis, the attenuation behavior of SL-RMLRPCs and DL-RMLRPCs for elastic waves at a finite period is evaluated by means of a frequency response function. Subsequently, a mass–spring equivalent model corresponding to of the SL-RMLRPCs and DL-RMLRPCs structure is developed for theoretically determining the bandgap range. The results indicate that the bandgap characteristics can be effectively improved by employing SL-RMLRPCs and DL-RMLRPCs compared with SOLRPCs, and the number and width of bandgaps of DL-RMLRPCs under multi-oscillator conditions are preferred to those of SL-RMLRPCs. The generation of the bandgap in both SL-RMLRPCs and DL-RMLRPCs originates from the transverse translational vibration and eccentric rotational vibration of the scatterer, which induces a strong coupling effect between the scatterer and the long-wavelength traveling wave in the matrix. Elastic wave frequencies located within the bandgap coverage are significantly hindered and suppressed during propagation. In comparison with SL-RMLRPCs, DL-RMLRPCs provide a more sustained and stable attenuation of low-frequency vibrational elastic waves. The mass–spring equivalent model possesses good accuracy and can quickly determine the bandgap range of SL-RMLRPCs and DL-RMLRPCs theoretically. This study can contribute to the theoretical reference for the optimal design of bandgap multi-range for local resonance composite structures.