悬臂梁挠曲电俘能器的力电耦合模型及性能分析

挠曲电效应指应变梯度在电介质中引起的电极化现象，是一种普遍存在的力电耦合行为。应变梯度与材料的尺寸成反比，因此挠曲电效应有望在纳米尺度主导材料的物理性质，尤其是力电耦合性能。本文建立了悬臂梁挠曲电俘能器的理论模型，基于哈密顿原理得到了悬臂梁挠曲电俘能器的控制方程和相应的边界条件；进一步，得到了悬臂梁挠曲电俘能器的输出电压频率响应和功率密度频率响应随悬臂梁的振动频率、外电路阻抗、挠曲电层厚度以及弹性层模量的变化规律。聚偏氟乙烯和环氧树脂层合挠曲电悬臂梁俘能器模型的数值结果表明输出电压频率响应和功率密度频率响应在共振频率点取得最大值，且随着各阶模态对应的共振频率的增加悬臂梁挠曲电俘能器的输出电压和功率密度均增加。此外，计算结果还表明悬臂梁俘能器存在最佳匹配阻抗，在匹配阻抗附近悬臂梁俘能器的输出功率密度随挠曲电层厚度的减小而增大，表现出明显的尺寸效应。本文工作提供了一种基于挠曲电效应的悬臂梁俘能器的理论模型，为悬臂梁俘能器的设计提供了理论依据。

Electromechanical coupling model and performance analysis of the unimorph cantilever beam-based flexoelectric energy harvester

Flexoelectric effect refers to the strain gradient induced electric polarization, and it is a universal electromechanical coupling effect in all solid dielectrics due to the inversion symmetry breaking by the strain gradient. Since the strain gradients are inversely proportional to the characteristic dimensional of materials, flexoelectric effect is expected to beyond the piezoelectric effect to dominant the electromechanical coupling phenomenon of materials at the nano scale. Mechanical Energy harvesters based on flexoelectric effect are considered one of the most promising applications in microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS). In the present work, a theoretical model for the flexoelectric energy harvester is established. The governing equations and corresponding boundary conditions are derived from the energy variation principle. In addition, the performance of the flexoelectric unimorph cantilever beam based energy harvester are analyzed based on the theoretical model. The effects of the resonance frequency, the resistance of the circuit, the thickness of the flexoelectric layer, and the Young’s modulus of the elastic layer on the output voltage frequency response and the output power density frequency response are discussed. Particularly, numerical analysis for cantilever beam based flexoelectric energy harvester fabricated by PVDF polymer thin film and epoxy substrate are obtained. It is found that the maximum output voltage frequency response and output power density frequency response appear at the resonance frequencies of the cantilever energy harvester. The output voltage and the output power density increase with the increase of the resonance frequencies at each mode. The numerical results also showed that there is an optimum resistance. Furthermore, the output power density increases with the decrease of the thickness of the flexoelectric layer when the resistance near its optimum value. Moreover, it is found that the output voltage decreases with the increase of the Young’s modulus of the elastic layer. The numerical results in this paper is helpful in designing cantilever beam-based flexoelectric energy harvesters.