Theoretical analysis of transverse and planar vibrations for the piezoceramic disk based on Mindlin plate theory

Abstract

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.