Abstract This paper combines negative capacitance (NC) with inductance (L) to enlarge low-frequency bandgap width in locally resonant piezoelectric metamaterials. The studied metamaterials are obtained by directly bonding patches on the surfaces of host structures, then connecting patches to shunts. Shunts with NC and L in series and in parallel are both studied. Analytical expressions of the bandgap ranges are derived, which reveal that the bandgap size is increased not simply because the NC enhancing the material’s electro-mechanical coupling factor, but in a more complicated way. Parametric studies are performed to analytically investigate the tuning properties of the LR bandgap by NC. Results demonstrate that by modifying NC value, the LR bandgap size can be significantly increased. Numerical simulations are done to verify the effects of the broadened bandgap on vibration transmission and reveal the limitations of the used analytical model. Practical implementation of the shunts are also discussed, recommendations on choosing the shunt configurations and NC values are given. This paper gives a theoretical guideline on designing piezoelectric metamaterials with bandgap effects at desired frequency ranges for practical applications like low-frequency vibration and noise reduction or isolation.

中文翻译：

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通过负电容扩大局部谐振压电超材料的低频带隙

摘要 本文结合负电容（NC）和电感（L）来扩大局部谐振压电超材料的低频带隙宽度。所研究的超材料是通过将贴片直接粘合在主体结构表面上，然后将贴片连接到分流器来获得的。研究了 NC 和 L 串联和并联的分流器。推导出带隙范围的解析表达式，表明带隙尺寸的增加不仅是因为 NC 增强了材料的机电耦合因子，而且是以更复杂的方式增加的。进行参数研究以分析研究 NC 对 LR 带隙的调谐特性。结果表明，通过修改 NC 值，可以显着增加 LR 带隙大小。进行数值模拟以验证加宽的带隙对振动传输的影响，并揭示所用分析模型的局限性。还讨论了分流器的实际实施，给出了选择分流器配置和 NC 值的建议。本文给出了设计在所需频率范围内具有带隙效应的压电超材料的理论指导，以用于低频振动和降噪或隔离等实际应用。