This work focuses on theoretical modeling and dynamic analysis of a flexoelectric beam energy harvester with the consideration of geometric nonlinearity. We assume that the beam energy harvester has a thickness at nanoscale and a width and length at microscale. Under a harmonic concentrated force, the proposed energy harvester generates electric power due to the phenomenon of flexoelectricity. Based on the theory of flexoelectricity and Euler–Bernoulli beam assumption, the nonlinear electromechanical coupling equations are derived. Galerkin method is employed to obtain the discrete nonlinear equations, which are then solved numerically. Frequency response curves are plotted to reveal the nonlinear characteristics of the energy harvester and it is found that the frequency response curves of the flexoelectric energy harvester exhibit hardening behaviors. Case studies are provided and we emphasize on the influences of load resistance, tip mass, concentrated force and damping ratio on the output performance of the energy harvester. In addition, it is suggested that the flexoelectric energy harvester has a better output performance under a square waveform force among different forms of the concentrated force. The results obtained are significant for designing optimal flexoelectric energy harvesters.

这项工作着重于考虑几何非线性的柔性电子束能量采集器的理论建模和动态分析。我们假设束能量采集器具有纳米级的厚度和微米级的宽度和长度。所提出的能量收集器在谐波集中力的作用下，由于柔电现象而产生电能。基于柔电理论和欧拉-伯努利梁假设，推导了非线性机电耦合方程。采用Galerkin方法获得离散非线性方程，然后对其进行数值求解。绘制频率响应曲线以揭示能量收集器的非线性特性，发现柔性电能量收集器的频率响应曲线表现出硬化行为。提供了案例研究，我们强调了负载阻力，叶尖质量，集中力和阻尼比对能量收集器输出性能的影响。另外，建议在不同形式的集中力中，在方波力的作用下，柔性电能采集器具有更好的输出性能。获得的结果对于设计最佳的柔性电能收集器具有重要意义。另外，建议在不同形式的集中力中，在方波力的作用下，柔性电能采集器具有更好的输出性能。获得的结果对于设计最佳的柔性电能收集器具有重要意义。另外，建议在不同形式的集中力中，在方波力的作用下，柔性电能采集器具有更好的输出性能。获得的结果对于设计最佳的柔性电能收集器具有重要意义。