Coupled vibration in hollow cylinders of longitudinally polarized piezoelectric ceramics

Abstract

Longitudinally polarized piezoelectric ceramic disks with central holes have been the most commonly used elements in underwater acoustics and ultrasonics. However, their vibrational characteristics and frequency spectra have not been thoroughly studied. In this paper, when the mechanical coupling coefficient is introduced and the shearing strain is ignored, an analytic method is presented. The coupled vibration of the longitudinally polarized piezoelectric ceramic disks with central holes is studied and the resonance frequency equations are derived. Based on the frequency equations, the longitudinal and radial resonance frequencies can be obtained when the dimensions and the material parameters are given. Compared with one-dimensional theory, the computed resonance frequencies in this paper are in good agreement with the measured results. Compared with the numerical methods, the analytic method presented in this paper is simple in computing the longitudinal and radial resonance frequencies and in analyzing the coupled vibrational modes of the piezoelectric ceramic disks with central holes.