Metastructures are engineered systems composed of periodic arrays of identical components, called resonators, designed to achieve specific dynamic effects, such as creating a band gap-a frequency range where waves cannot propagate through the structure. When equipped with patches of piezoelectric material, these metastructures exhibit an additional capability: they can harvest energy effectively even from frequencies much lower than the fundamental frequency of an individual resonator. This energy harvesting capability is particularly valuable for applications where low-frequency vibrations dominate. To support the design of metastructures for dual purposes, such as energy harvesting and vibration suppression (reducing unwanted oscillations in the structure), we develop a multi-patch isogeometric model of a piezoelectric energy harvester. This model is based on a piezoelectric Kirchhoff-Love plate-a thin, flexible structure with embedded piezoelectric patches-and uses Nitsche's method to enforce compatibility conditions in terms of displacement, rotations, shear force, and bending moments across the boundaries of different patches. The model is validated against experimental and numerical data from the literature. We then present a novel, parameterized metastructure plate design and conduct a parametric study to explore how resonator geometries affect key performance metrics, including the location and width of the band gap and the position of the first peak in the voltage frequency response function. This model can be integrated with optimization algorithms to maximize outcomes such as energy harvesting efficiency or vibration reduction, depending on application needs.

翻译：超结构是由周期性排列的相同组件（称为谐振器）构成的工程系统，旨在实现特定的动力学效应，例如产生带隙——即波无法在结构中传播的频率范围。当配备压电材料贴片时，这些超结构展现出额外的能力：即使频率远低于单个谐振器的基频，它们也能有效收集能量。这种能量收集能力在低频振动占主导地位的应用中尤其有价值。为支持超结构在能量收集与振动抑制（减少结构中不必要的振荡）双重用途的设计，我们开发了一种压电能量收集器的多片等几何模型。该模型基于压电基尔霍夫-洛夫板——一种嵌入压电贴片的薄型柔性结构——并采用尼切方法在位移、转角、剪切力和弯矩方面对不同贴片边界施加相容性条件。该模型通过文献中的实验和数值数据进行了验证。随后，我们提出了一种新颖的参数化超结构板设计，并进行了参数化研究，以探索谐振器几何形状如何影响关键性能指标，包括带隙的位置和宽度以及电压频率响应函数中第一峰值的位置。该模型可与优化算法结合，根据应用需求最大化能量收集效率或振动抑制效果等目标。