压电介质表面圆形电极边缘的电-弹场分析

Electro-Elastic Fields Arising near Circular Electrode Border on Piezoelectric Medium Surface

基于线性压电理论 ,研究了表面附有圆形电极板的半无限压电介质电极边缘的电弹场奇异分布特性。利用Hankel变换技术 ,将空间轴对称混合边值问题简化为一组对偶积分方程的求解 ,并得到了应力分量和电位移分量的解析表达式。算例表明在电极边缘的邻域内存在剧烈的应力集中和电位移增强 ,足以造成介质的脆性断裂或介质击穿。并对这种类裂纹奇异性质进行了讨论。

Based on linear piezoelectricity, the singularly distributed stresses and electric displacement in the surface electrode border vicinity are investigated. Hankel transform is adopted to reduce the spacially axisymmetric problem with mixed boundary conditions into a pair of dual integral equations. And the components of stress and electric displacement are solved analytically. A numerical example reveals that strongly concentrated stresses and extremely intensified electric displacements near the electrode border are high enough to puncture or fracture the piezoelectric medium. The 'like crack' features are discussed in some detail.