Abstract Phononic crystal (PnC)-based piezoelectric energy harvesting (PEH) has been recently introduced to amplify the input energy fed into PEH devices. If a defect is imposed into a PnC, as a result, defect bands are created within the band gap. At a defect band frequency, elastic waves can be localized inside the defect. By attaching a PEH device to the defect, output electric power can be significantly enhanced. However, since the attachment of the PEH device leads to the shifting of the defect band frequency, the output electric power can drop significantly if an excitation frequency does not align with the shifted defect band frequency. Thus, this study aims to develop an electroelastically coupled analytical model of a PnC with a piezoelectric defect; the proposed model considers the inertia and stiffness effects. An electroelastically coupled transfer matrix is derived by simultaneously solving a mechanical equation of motions and an electrical circuit equation, with the help of Green's function. The proposed electroelastically coupled analytical model can be used to predict defect band frequencies and defect mode shapes (based on a transfer matrix method; TMM) and output electric power (based on an S-parameter method; SPM) across an external electrical resistance. Results of the proposed electroelastically coupled analytical model are in very good agreement with those of a finite element method (FEM). The contributions of the proposed electroelastically coupled analytical model are two-fold: (1) this is the first attempt to propose analytical model of a PnC with a piezoelectric defect for energy harvesting; and (2) the model allows physical parameterization of the electroelastically coupled transfer matrix in an explicit manner.

中文翻译：

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具有压电缺陷的声子晶体的分析模型，用于使用电弹性耦合传递矩阵进行能量收集

摘要 最近引入了基于声子晶体 (PnC) 的压电能量收集 (PEH) 来放大馈入 PEH 设备的输入能量。如果缺陷被强加到 PnC 中，则结果是在带隙内产生缺陷带。在缺陷带频率下，弹性波可以定位在缺陷内部。通过在缺陷处安装 PEH 器件，可以显着提高输出电力。然而，由于PEH器件的连接导致缺陷带频率的偏移，如果激励频率与偏移的缺陷带频率不一致，则输出电功率会显着下降。因此，本研究旨在开发具有压电缺陷的 PnC 的电弹性耦合分析模型；建议的模型考虑了惯性和刚度的影响。在格林函数的帮助下，通过同时求解运动的机械方程和电路方程，推导出电弹性耦合传递矩阵。所提出的电弹性耦合分析模型可用于预测缺陷带频率和缺陷模式形状（基于传递矩阵方法；TMM）和外部电阻上的输出电功率（基于 S 参数方法；SPM）。所提出的电弹性耦合分析模型的结果与有限元方法 (FEM) 的结果非常吻合。所提出的电弹性耦合分析模型的贡献有两个方面：（1）这是首次尝试提出具有用于能量收集的压电缺陷的 PnC 分析模型；