Analysis of tonpilz with flexing pistons.

The acoustic loading of each of the first six modes of a double piston piezoelectric stack‐driven underwater acoustic transducer is found using Botman’s method [NAA report NA65H‐1024, June 1965] revised with the use of the Helmholtz integral formulation of Chertok [J. Acoust. Soc. Am. 36, 1305–1313 (1964)]. Both self and mutual impedances are obtained and the admittance of each mode solved for. Finite element analysis is used to determine the mode parameters of the first 30 modes and the contribution to compliance loading of modes 7‐30. Using symmetry, the eight‐element stack is represented by a ten‐mesh circuit that includes joint compliances, end piece masses, a distributed parameter representation of the stressbar, and the contact compliances between end pieces and pistons. Input impedance and total radiated power are computed for a wide range of frequencies. For joint compliance of the order of 0.25 E–10 M/N or less, a simpler stack model is found to be adequate.