In this work, the static and dynamic response of a piezoelectric semiconductor cantilever under the transverse end force with consideration of flexoelectricity and strain gradient elasticity is systematically investigated. The one-dimensional governing equations and the corresponding boundary conditions are derived based on Hamilton’s principle. After that, combining with the linearized equations for the conservation of charge, the effects of characteristic length and flexoelectric coefficient on the working performance of a ZnO nanowire are demonstrated as a numerical case, including the static mechanical and electric fields, natural frequencies, and the frequency–response characteristics at resonances. The results indicate that the flexoelectric effect has a great influence on the electric properties of the nanowire, while the strain gradient effect directly contributes to its mechanical properties. To some extent, the increase in characteristic length is equivalent to the stiffness strengthening. The qualitative results and quantitative data are beneficial for revealing the underlying physical mechanism and provide guidance for the design of piezoelectric semiconductor devices.

在这项工作中，系统地研究了压电半导体悬臂在横向端力作用下的静态和动态响应，同时考虑了挠性电和应变梯度弹性。根据汉密尔顿原理导出一维控制方程和相应的边界条件。之后，结合线性化方程以节省电荷，以数值形式证明了特征长度和柔电系数对ZnO纳米线工作性能的影响，包括静态机械和电场，固有频率和共振时的频率响应特性。结果表明，柔电效应对纳米线的电性能有很大的影响，而应变梯度效应直接影响其力学性能。在某种程度上，特征长度的增加等同于刚度的增强。定性结果和定量数据有助于揭示潜在的物理机理，并为压电半导体器件的设计提供指导。