The natural vibrational modes of axially symmetric piezoelectric ceramic disks have been calculated by the finite-element method. The disks are of the type used as active elements in compressional wave ultrasonic transducers, and are electrically polarized in thickness with full electrodes on the disk's major faces. To optimize disk geometry for ultrasonic transducer application, the dependence of the vibrational modes on the disk diameter-to-thickness ratio for ratios from 0.2 (a tall cylinder) to 10.0 (a thin disk) has been studied. Series and parallel resonance frequencies for each of the modes are determined through an eigenfrequency analysis, and effective electromechanical coupling coefficients are calculated. The modal displacement fields in the disk are calculated to determine the physical nature of each mode. An analysis of the complete spectrum of piezoelectrically active modes as a function of diameter-thickness ratio is presented for the ceramic PZT-5H, including and identification of radial, edge, length expander, thickness shear, and thickness extensional vibrations. From this analysis, optimal diameter-to-thickness ratios for good transducer performance are discussed.

We have calculated the natural vibrational modes of fully electroded, axially symmetric piezoelectric ceramic disks by the finite element method. We have studied the dependence of the vibrational modes on the disk diameter/thickness ratio for ratios from 0.2 (a tall cylinder) to 10.0 (a thin disk). Series and parallel resonance frequencies and effective electromechanical coupling coefficients are calculated for each of the modes. The modal displacement fields in the disk are calculated for selected modes. The complete spectrum of piezoelectrically active modes as a function of diameter/thickness ratio d / t is presented for the ceramic PZT-5H' , including an identification of radial, edge, length expander, thickness shear, and thickness extensional vibrational modes. Optimal diameter/thickness ratios are discussed.