挠曲电效应对简支梁式压电传感器性能的影响

The Effect of Flexoelectricity on Performance of Simple Support Beam Piezoelectric Sensors

挠曲电效应是材料极化强度(或电场强度)与应变梯度之间的耦合关系,对于新型微纳米致动器和传感器的性能具有重要的影响.以纳米简支梁式压电传感器(简称压电简支梁)为研究对象,讨论材料的挠曲电效应对压电简支梁输出电势与挠度的影响.采用电吉布斯自由能密度函数,并根据压电材料线性理论与伯努利-欧拉梁理论,采用变分法推导压电简支梁的控制方程和相应力电耦合边界条件.数值模拟BaTiO3压电简支梁在外加机械载荷作用下,由于挠曲电效应产生的诱导电势和极化强度等与梁结构、材料参数的相互关系.计算结果表明,诱导电势反馈作用在梁的表面引起一个与机械载荷作用相反的弯矩,减小了梁结构的弯曲挠度;在一定的挠曲电系数和梁结构尺寸下,诱导电势存在最大值;在微纳尺度上挠曲电效应具有很强的尺寸依赖性,随着梁的厚度增大,挠曲电效应的影响将显著减弱.

The flexoelectric effect is the coupling between the polarization （or electric tield） anportant influence on the new micro-nano actuator and sensor.In this paper, the simply supported piezoelectric used to study the effect of flexoelectricity on the induced electric potential and deflection of sensors.Based onenergy density function,the linear piezoelectric theory and the Bernoulii-Euler beam theory,the governing equations and the boundary conditions are deduced by the variation method.Using numerical simulations ？ the relationships betweenpolarization and thematerial parameters/structure sizes of BaTiO3 simplesupport sensors havebeen obtained under the mechanical loading.These results show that the induced electric potential due to the flexoelectricity causes a reversed moment, which opposesthose mechanically induced and decreases the deflection of the beams.The maximum induced electric potential expriate flexoelectric coeflicient and beam thickness.The results also ^how that the flexoelectric effect has a strong size-dependent on micro- nanoscale. With the thickness of the BaTiO3 piezoelectric nanobeam increasing, the effect of flexoelectricity decreases signili-cantly.