中文摘要：

提出了一种轴向极化压电圆环和圆片的径厚二维耦合等效电路模型。应用这一模型分析了它们的耦合振动，比较了不同尺寸比例下耦合振动与单一模式振动的异同，发现这种方法比一维等效电路方法能在较宽尺寸范围内更准确的分析压电振子的振动问题。有限元计算和试验测量结果验证了这一模型对压电振子频率计算的准确性。

英文摘要：

A 2-D equivalent circuit models of the longitudinally polarized annulus and circular piezoelectric disk are established, which is coupled in the thickness and radial direction. Based on this, their coupled vibration is analyzed and the difference between the coupled vibration and the singular-mode vibration on various aspect ratios is identified. It is found that this modal is more accurate in vibration analysis of piezoceramic elements than the one-dimensional one in more wide range of aspect ratios. The FEM and measured results validated the accuracy of this model in frequency calculation of piezoceramic elements.