FINITE-ELEMENT ANALYSIS OF VIBRATIONAL-MODES IN PIEZOELECTRIC CERAMIC DISKS

The natural vibrational modes of axially symmetric piezoelectric ceramic disks by the finite-element method have been calculated. The disks are of the type employed as active elements in com-pressional 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 an 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. © 1990 IEEE