Elastic-electro-mechanical modeling and analysis of piezoelectric metamaterial plate with a self-powered synchronized charge extraction circuit for vibration energy harvesting

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 (Lr) parallel with the clamped capacitor (Cp) of the piezoelectric patch, we can see that a new dispersion curve is induced by the Lr-Cp 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.