《厦门大学学报（自然科学版）》

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 field)and the strain gradient,which has important influence on the new micro-nano actuator and sensor.In this paper,the simply supported piezoelectric nanobeams have been used to study the effect of flexoelectricity on the induced electric potential and deflection of sensors.Based on the electric Gibbs free energy density function,the linear piezoelectric theory and the Bernoulli-Euler beam theory,the governing equations and the boundary conditions are deduced by the variation method.Using numerical simulations,the relationships between the induced electric potential/polarization and the material parameters/structure sizes of BaTiO3 simple support sensors have been obtained under the mechanical loading.These results show that the induced electric potential due to the flexoelectricity causes a reversed moment,which opposes those mechanically induced and decreases the deflection of the beams.The maximum induced electric potential exists with the appropriate flexoelectric coefficient and beam thickness.The results also show 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 significantly.

引言
1 本构方程的推导
2 压电简支梁控制方程的建立与求解
3 数值计算与讨论
4 结论

图1 压电简支梁的示意图<br/>Fig.1 Configuration of a piezoelectric beam with simple support model

图1 压电简支梁的示意图
Fig.1 Configuration of a piezoelectric beam with simple support model

图2 不同挠曲电系数下诱导电势与厚度的关系曲线<br/>Fig.2 Variation of the induced electric potential with the beam thickness for different flexoelectric coefficients

图2 不同挠曲电系数下诱导电势与厚度的关系曲线
Fig.2 Variation of the induced electric potential with the beam thickness for different flexoelectric coefficients

图3 不同厚度梁的归一化等效挠度曲线<br/>Fig.3 Variation of the normalized deflection for the different beam thicknesses

图3 不同厚度梁的归一化等效挠度曲线
Fig.3 Variation of the normalized deflection for the different beam thicknesses

表1 不同挠曲电系数与梁厚度组合下的最优诱导电势<br/>Tab.1 The optimal induced potential with the flexoelectric coefficients and thicknesses

表1 不同挠曲电系数与梁厚度组合下的最优诱导电势
Tab.1 The optimal induced potential with the flexoelectric coefficients and thicknesses

图4 不同挠曲电系数下梁中点的归一化等效挠度随厚度的变化曲线<br/>Fig.4 Variation of normalized deflection at the midpoint with beam thickness for different flexoelectric coefficients

图4 不同挠曲电系数下梁中点的归一化等效挠度随厚度的变化曲线
Fig.4 Variation of normalized deflection at the midpoint with beam thickness for different flexoelectric coefficients

图5 不同挠曲电系数下归一化等效刚度随厚度的变化曲线<br/>Fig.5 Variation of normalized effect stiffness with beam thickness for different flexoelectric coefficients

图5 不同挠曲电系数下归一化等效刚度随厚度的变化曲线
Fig.5 Variation of normalized effect stiffness with beam thickness for different flexoelectric coefficients

图6 不同挠曲电系数下梁内不同截面上极化强度随厚度的变化曲线<br/>Fig.6 Variation of the polarization at different sections with the beam thickness for different flexoelectric coefficients

图6 不同挠曲电系数下梁内不同截面上极化强度随厚度的变化曲线
Fig.6 Variation of the polarization at different sections with the beam thickness for different flexoelectric coefficients

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备注

引言

1 本构方程的推导

2 压电简支梁控制方程的建立与求解

3 数值计算与讨论

4 结论

学报简介

备注

引言

1 本构方程的推导

2 压电简支梁控制方程的建立与求解

3 数值计算与讨论

4 结 论

学报简介

4 结论