压电体扭转效应研究

Investigation on torsion effect of piezoelectrics

初步探讨了压电体的扭转效应 .应用弹性理论、压电理论分析了压电体内的扭转应力及由其所导致的非线性极化状态 .由电动力学理论得知 ,极化将会在空间产生电场 .根据电场的等效原理 ,极化梯度的存在 ,不仅在压电体表面上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聚集 .从麦克斯韦方程组及矢量分析出发 ,推导得到了束缚电荷激发的电场所满足的偏微分方程 .通过引入静电场的标量位函数 ,将电场强度的矢量泊松方程转化为位势的椭圆型偏微分方程的诺依曼边值问题 .采用有限元法求解得到了束缚电荷产生的电场强度在压电体内及边界上的分布 ,得到了迥异于线性极化的结果 .根据导体在电场中的边界条件分析 ,有效地在压电体表面布置了检测电极 .理论分析结论得到了实验结果的有力支持 ,并将为单压电体扭矩测量技术奠定基础 .

The concept of the torsional effect of piezoelectrics is first proposed in this article. The stresses caused by the mechanical torque on the piezoelectric bar are deduced by using the energy method in the elastic theory and the accompanying non-linear polarization in the piezoelectric body is analyzed. In the viewpoint of electrodynamics, the equivalent bound volume charges will accumulate in the piezoelectric body in addition to the bound surface charges considering the effect of the polarization gradient. The vectorial partial differential equation which the electric field intensity satisfies is deduced by applying Maxwell equations to the situation considered. And the problem is converted to the typical Neumann boundary value problem for the elliptic equations by inducing the scalar potential function. The distribution of the electric field intensity in the piezoelectric body is obtained by the finite element method. The measuring electrodes are effectively disposed on the surfaces of the piezoelectric body based on the analysis of the boundary condition of conductors in the electric field. The investigation in this article would establish the basis for the torque measuring technique on the single piezoelectric body.