Flexoelectric materials have played an increasingly vital role in nanoscale sensors, actuators, and energy harvesters due to their scaling effects. In this paper, the nonlocal effects on flexoelectric nanosensors are considered in order to investigate the coupling responses of beam structures. This nonlocal elasticity theory involves the nonlocal stress, which captures the effects of nonlocal and long-range interactions, as well as the strain gradient stress. Based on the electric Gibbs free energy, the governing equations and related boundary conditions are deduced via the generalized variational principle for flexoelectric nanobeams subjected to several typical external loads. The closed-form expressions of the deflection and induced electric potential (voltage) values of flexoelectric sensors are obtained. The numerical results show that the nonlocal effects have a considerable influence on the induced electric potential of flexoelectric sensors subjected to general transverse forces. Moreover, the induced electric potential values of flexoelectric sensors calculated by the nonlocal model may be smaller or larger than those calculated by the classical model, depending on the category of applied loads. The present research indicates that nonlocal effects should be considered in order to understand or design basic nano-electromechanical components subjected to various external loads.

中文翻译：

---

基于非局部弹性理论的柔性纳米电传感器的机电分析

柔性电材料由于其缩放作用而在纳米级传感器，致动器和能量收集器中发挥着越来越重要的作用。为了研究梁结构的耦合响应，考虑了非局部效应对柔性纳米传感器的影响。这种非局部弹性理论涉及非局部应力，该非局部应力捕获了非局部和远距离相互作用的影响以及应变梯度应力。基于吉布斯电自由能，通过广义变分原理推导了柔性电纳米束在几种典型外部载荷作用下的控制方程和相关边界条件。获得挠性电传感器的挠度和感应电势（电压）值的闭合形式。数值结果表明，非局部效应对受一般横向力作用的挠性电传感器的感应电势有相当大的影响。此外，取决于所施加负载的类别，由非局部模型计算出的柔性电传感器的感应电势值可以小于或大于经典模型计算出的那些。本研究表明，应考虑非局部效应，以理解或设计承受各种外部载荷的基本纳米机电组件。非局部模型计算得出的柔性电传感器的感应电势值可以小于或大于经典模型计算得出的值，具体取决于所施加负载的类别。本研究表明，应考虑非局部效应，以理解或设计承受各种外部载荷的基本纳米机电组件。非局部模型计算得出的柔性电传感器的感应电势值可以小于或大于经典模型计算得出的值，具体取决于所施加负载的类别。本研究表明，应考虑非局部效应，以理解或设计承受各种外部载荷的基本纳米机电组件。