A comparison of models for a piezoelectric 31-mode segmented cylindrical transducer

Piezoelectric transducers with cylindrical geometry are often designed to operate in a radial “breathing” mode. In order to tune their performance in a cost effective way, cylinders can be constructed of alternating active (piezoelectric) and inactive (non-piezoelectric) staves. Existing lumped parameter models for such a ring are based on effective piezoelectric properties of the composite ring which reduce the system to a single degree of freedom corresponding to the breathing motion. Unfortunately, if the length of the staves is a sufficiently large percentage of the circumference, the transducer may demonstrate a detrimental higher frequency resonance within the desired bandwidth of operation even when all staves are uniformly excited by an electrical field. This parasitic resonance results from bending motion of the staves associated with stiffness and mass discontinuities of the constituent material properties and can significantly decrease the radiated acoustic pressure and generate distortion of the radiated acoustic waveform. This work presents a multiple-degree-of-freedom lumped parameter model that captures both the breathing and bending resonances of the transducer and provides a more accurate prediction of its effective coupling coefficient. Results are compared with a one-degree-of-freedom model, finite element models, and experimental data. Modifications to account for internal volumes, nonlinearities, and other effects are also presented and discussed.