The flexoelectric effect can be enhanced at the micro/nanoscale due to its size-dependency, so it is more suitable for energy harvesting than piezoelectric energy harvesters. To enhance the energy harvesting performance, this paper theoretically investigates the energy harvesting characteristics of micro circular plates with variable material properties and with consideration of the flexoelectric effect. The energy variational principle is resorted to formulate the governing equations of double-layer Kirchhoff micro circular plates, which then the analytical solutions of mechanical and electrical responses are solved. The theoretical model is validated by comparing with simulation results obtained from COMSOL Multiphysics. Furthermore, the parameter studies are addressed to discuss the influence of radial gradient index, resistance, and geometric parameters. Numerical results show that the size effect and the radial gradient distributions significantly influence the frequency response and the energy conversion efficiency. Compared with the homogeneous flexoelectric structure, the maximum power density of the proposed model is greatly improved. This research provides fundamental theoretical support and is helpful to design high-performance nanoscale energy harvesters.

由于其尺寸依赖性，可以在微/纳米尺度上增强挠曲电效应，因此它比压电能量收集器更适合能量收集。为了提高能量收集性能，本文从理论上研究了具有可变材料特性的微圆板的能量收集特性，并考虑了挠曲电效应。利用能量变分原理，建立了双层基尔霍夫微圆板的控制方程，求解了机械响应和电响应的解析解。通过与从 COMSOL Multiphysics 获得的仿真结果进行比较，对理论模型进行了验证。此外，参数研究旨在讨论径向梯度指数、阻力、和几何参数。数值结果表明，尺寸效应和径向梯度分布显着影响频率响应和能量转换效率。与均质挠电结构相比，所提出模型的最大功率密度得到了极大的提高。该研究提供了基础理论支持，有助于设计高性能纳米级能量收集器。