压电扭转问题中非线性极化分析及电场检测

应用弹性理论、压电理论分析了压电体内的应力状态及由其所导致的非线性极化状态。由于极化梯度的存在，不仅在压电体的表面上会产生等效面束缚电荷，在压电体内部同时也会有等效体束缚电荷的聚集。以矩形截面石英柱体为例，选取级数形式的应力函数，采用能量法及根据电场的等效原理推导了由扭转而产生的剪应力和面束缚电荷密度及体束缚电荷密度的解析表达式，得到了迥异于线性极化的结果。采用有限元方法计算了束缚电荷产生的电场。建立了机械扭矩同检测电极的输出电量之间的线性关系，并实现了单压电体扭矩检测。

Analysis and Detection of Nonlinear Polarization in Torsion of Piezoelectric Cylinder

The stresses caused by mechanical torque on piezoeletric bar are deduced by using energy method in elastic theory and the accompanying nonlinear polarization in the piezoelectric body is analysed.In electrodynamics point of view equivalent bound volume charges will accum ulate in the piezoelectric body in addition to the bound surface charges considering the effect of polarization gradient.The distribution of the electric field intensity in the piezoelectric body is obstained by finite element method.The m easuring electrodes are effectively disposed on the surfaces of the piezoelectric body based on the analysis of boundary condition of conductors in electric field.The in- vestigation in this article would establish the basis for torque m easuring technique on single piezoelectric body.