Extending bandgap method of concentric ring locally resonant phononic crystals

Locally resonant phononic crystals (LRPCs) have the capacity to adjust elastic waves with the structure sizes much smaller than the incident wavelengths, the unique property is called low-frequency bandgap, but it is not easily applied in practical engineering because of narrow bandgap width. Multilayered LRPCs are helpful in generating several bandgaps, in the meanwhile the designs of multilayered LRPCs proposed in previous study result in the larger filling fraction, whereas the bandwidth of LRPCs increases monotonically with filling fraction, thus the pure contribution of concentric ring configuration to the bandwidth extending is less involved. Keeping the filling fraction constant, this paper carefully designs the microstructure of concentric ring locally resonant phononic crystals, and investigates the effects of structure configuration on the bandgap property. To this end, an updated improved plane wave expansion (UIPWE) method is developed to calculate the band structure, and finite element method (FEM) is used to obtain transmission spectra and vibration mode. The results demonstrate that UIPWE method is valid and is able to give precise outcomes, which is verified by FEM. In addition, the concentric ring configuration equivalently produces dual-oscillator system, relative movements between the oscillators generate coupling effect, thus, the bandgaps can be extended by configurating rightly the microstructure of single cell. Further studies about different models indicate that the combination of smaller inner scatterers and larger inner coating layers are beneficial to wider bandgap. These conclusions presented herein provide insights in the design of three-component PCs in multi-frequency vibration control field.