Vibration characteristics of a piezoelectric disk laminated with an elastic disk

This paper theoretically and experimentally deals with the vibration characteristics of a piezoelectric disk polarized in the thickness direction and laminated with an elastic disk. Axisymmetric vibration modes include radial and axial motions. Theoretically, in this study, the differential equations of piezoelectric motions were derived in terms of radial and axial displacements and electric potential. The differential equations of elastic motions were expressed in terms of radial and axial displacements. Solving the governing equations and boundary conditions for a coupled structure produced 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 finiteelement analysis and experiments; moreover, the theoretical analysis was verified on the basis of this comparison. It appeared that the natural frequencies of the radial modes of the piezoelectric disk were not affected by the elastic disk; however, those of the thickness modes were reduced by the elastic disk owing to the added mass effect.