Dynamic characteristics of piezoelectric cylindrical transducers with radial polarization

This paper presents the radial vibration characteristics of piezoelectric cylindrical transducers. Taking into account the piezoelectric anisotropy, dynamic differential equations of piezoelectric radial motion have been derived in terms of radial displacement and electric potential. Applying mechanical and electric boundary conditions has yielded a characteristic equation for radial vibration of the radially polarized piezoelectric cylinder. Theoretical calculations of the fundamental natural frequency have been compared with numerical and experimental results for transducers of several sizes, and have shown a good agreement.