悬臂梁挠曲电俘能器的力电耦合模型及性能分析

Flexoelectric effect refers to the strain-gradient-induced electric polarization, which is a universal electromechanical coupling effect in all solid dielectrics due to the breaking of inversion symmetry by strain gradient. Since strain gradients are inversely proportional to the dimensional characteristics of materials, the electromechanical coupling phenomenon of materials at nanoscale is expected to be dominated by the flexoelectric effect, instead of the piezoelectric effect. The 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 is analyzed based on the theoretical model. The effects of resonance frequency, resistance of circuit, thickness of flexoelectric layer, and Young's modulus of elastic layer on the output voltage frequency response and output power density frequency response are discussed. Particularly, the numerical analysis for cantilever beam-based flexoelectric energy harvester fabricated by PVDF polymer thin film and epoxy substrate is 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 show that there exists an optimum resistance. Furthermore, the output power density increases with the decrease of the thickness of flexoelectric layer when the resistance is close to its optimum value. Moreover, it is found that the output voltage decreases with the increase of the Young's modulus of elastic layer. The numerical results in this paper can be helpful in designing cantilever beam-based flexoelectric energy harvesters.