Piezoelectric ceramic stacks for underwater transducers

An analytical model is presented of a stack of annular rings used in underwater Tonpilz and Flextensional transducers to radiate high acoustic power. The length of each ring is much less than the average diameter. The model is based on exact solutions to exact piezoelectric governing equations for rings. Boundary and continuity conditions are satisfied in an average sense. It is shown that the computed resonance frequencies are more accurate than those obtained using a one-dimensional model by comparing them with those obtained using ATILA - a finite element package.