Abstract Structural vibrations usually exist in the form of low-frequency and broadband elastic waves, so cantilever-like harvesters are not appropriate due to space limitations and high quality factor. Piezoelectric metamaterial plate with local resonators (PMP-LR) has been explored to overcome it. However, how to model and analyze the whole energy harvesting system is still a challenge. In this paper, a self-powered synchronized charge extraction circuit is presented and connected to the PMP-LP as the interface circuit. An elastic-electro-mechanical model is built based on the Kirchhoff plate theory and equivalent impedance method, where equivalent impedance of the self-powered synchronized charge extraction circuit is first derived. Then the elastic-electro-mechanical model is numerically solved by using the Bloch theorem and wave finite element method. By numerical simulations, it is found that the synchronized charge extraction circuit has few effects on vibration bandgaps of the PMP-LR. While by inserting an inductor ( L r ) parallel with the clamped capacitor ( C p ) of the piezoelectric patch, we can see that a new dispersion curve is induced by the L r - C p electrical resonance and the inductor is beneficial for low-frequency and broadband vibration energy harvesting. In particular, the inductor can greatly improve the harvesting performance when the resonant frequency is equal to the excitation frequency. In the end, experiments are done and the results are consistent with the numerical ones. Excitingly, the output voltage amplitude of the piezoelectric patch is enlarged about 200% after using the resonant inductor.

中文翻译：

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具有自供电同步电荷提取电路用于振动能量收集的压电超材料板的弹性机电建模与分析

摘要 结构振动通常以低频和宽带弹性波的形式存在，因此由于空间限制和高品质因数，悬臂式采集器并不适用。已经探索了具有局部谐振器的压电超材料板 (PMP-LR) 来克服它。然而，如何对整个能量收集系统进行建模和分析仍然是一个挑战。在本文中，提出了一种自供电同步电荷提取电路，并将其连接到 PMP-LP 作为接口电路。基于基尔霍夫板理论和等效阻抗法建立弹性机电模型，首先推导出自供电同步电荷提取电路的等效阻抗。然后利用Bloch定理和波动有限元方法对弹性机电模型进行数值求解。通过数值模拟发现，同步电荷提取电路对PMP-LR的振动带隙影响很小。而通过在压电贴片的钳位电容器 (C p ) 上插入一个电感器 ( L r )，我们可以看到 L r - C p 电谐振引起了一条新的色散曲线，电感器有利于低-频率和宽带振动能量收集。特别是当谐振频率等于激励频率时，电感可以大大提高收集性能。最后进行了实验，结果与数值一致。令人兴奋的是，