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.

中文翻译：

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同心环局部共振声子晶体的扩展带隙方法

局域共振​​声子晶体（LRPCs）具有调节弹性波的能力，其结构尺寸远小于入射波长，这种独特的特性被称为低频带隙，但由于带隙宽度窄，在实际工程中不易应用。多层 LRPC 有助于产生多个带隙，同时先前研究中提出的多层 LRPC 的设计导致更大的填充率，而 LRPC 的带宽随填充率单调增加，因此纯同心环配置对带宽的贡献扩展较少涉及。在保持填充率不变的情况下，本文精心设计了同心环局部共振声子晶体的微观结构，并研究了结构配置对带隙特性的影响。为此，开发了一种更新的改进平面波展开（UIPWE）方法来计算能带结构，并使用有限元方法（FEM）获得透射谱和振动模式。结果表明 UIPWE 方法是有效的并且能够给出精确的结果，这得到了 FEM 的验证。此外，同心环配置等效产生双振荡器系统，振荡器之间的相对运动产生耦合效应，因此，可以通过正确配置单电池的微观结构来扩展带隙。对不同模型的进一步研究表明，较小的内部散射体和较大的内部涂层的组合有利于更宽的带隙。