In this paper, the out-of-plane and in-plane displacements coupled behavior of the transverse and planar vibration characteristics for piezoceramic disks under fully-clamped and traction-free boundary conditions are investigated theoretically base on the Mindlin's and Kirchhoff's plate models. By varying the radius-to-thickness ratios, the piezoceramic disks with moderate and thin thickness are considered in the analysis. It is verified that Mindlin's plate theory with first-order shear deformation hypothesis provides sufficient accuracy for transverse vibration analysis in comparison with Kirchhoff's model; however, this circumstance does not occur for planar vibration analysis. With the aid of theoretical analysis, both the resonant frequency and the corresponding mode shape are obtained for piezoceramic disks with various radius-to-thickness ratios. In addition, maximum normalized displacement components in three directions are also explored to identify the coupled vibration modes. Numerical calculations using the finite element method (FEM) are performed and the results are compared with the theoretical analysis. Excellent consistence between the theoretical and numerical results are found for the three-dimensional coupled vibration characteristics of piezoceramic disks.

本文基于Mindlin和Kirchhoff平板模型，从理论上研究了压电陶瓷盘在完全夹紧和无牵引边界条件下的平面和平面内位移耦合横向和平面振动特性的行为。通过改变半径与厚度的比率，在分析中考虑了厚度适中且薄的压电陶瓷盘。验证了与一阶剪切变形假设有关的Mindlin板理论与Kirchhoff模型相比，为横向振动分析提供了足够的准确性；但是，这种情况在平面振动分析中不会发生。借助理论分析，对于具有各种半径-厚度比的压电陶瓷盘，均获得了谐振频率和相应的模态形状。此外，还探索了三个方向上的最大归一化位移分量，以识别耦合振动模式。使用有限元方法（FEM）进行了数值计算，并将结果与​​理论分析进行了比较。压电陶瓷盘的三维耦合振动特性在理论和数值结果之间具有极好的一致性。