Vibration characteristics of a piezoelectric transducer laminated with piezoelectric disks

This paper considers a piezoelectric transducer polarized in the thickness direction and laminated with a piezoelectric disk. Its vibration characteristics were investigated theoretically and experimentally in the scope of the radial and axial motions in axisymmetric vibration modes. Theoretically, the differential equations of piezoelectric motions were derived in terms of radial and axial displacements and electric potential, and they were solved to produce characteristic equations that provided natural frequencies and mode shapes. Experimentally, the natural frequencies were measured using an impedance analyzer and the radial in-plane motions of the fundamental mode were measured using an in-plane laser interferometer. The results of the theoretical analysis were compared with those of a finite-element analysis and experiments, and the theoretical analysis was verified on the basis of this comparison. It appeared that the natural frequencies of the radial modes of the piezoelectric transducer were not affected by the added piezoelectric disk; however, those of the thickness modes were reduced by the piezoelectric disk owing to the added mass effect.