Coupled vibration analysis of the thin-walled cylindrical piezoelectric ceramic transducers

Analysis of electromechanical transducers employing axially symmetric vibrations of piezoelectric ceramic thin-walled tubes of arbitrary aspect ratio is presented based on application of the energy method [B. S. Aronov, J. Acoust. Soc. Am. 117, 210-220 (2005)]. The suggestion made by Giebe and Blechshmidt [Ann. Physik, Ser. 5 18, 417-485 (1933)] regarding representation of a tube vibration as a coupled vibration of two partial systems is used to choose the assumed modes of the piezoceramic tube vibration, and the energy of the flexural deformations accompanying the extensional vibration of a tube is also taken into consideration. The Lagrange type equations describing the transducer vibrations are derived, and the equivalent electromechanical circuit is introduced that conveniently represents the solution. The resonance frequencies, effective coupling coefficients, and velocity distributions for differently poled piezoceramic tubes as functions of their height-to-diameter aspect ratio are calculated. The validity of the equivalent circuit is extended to the case that a piezoceramic tube is mechanically and acoustically loaded on the ends and acoustically loaded on its outer surface. The results of calculations are in good agreement with the results of experimental investigations.