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The variational principle is an approximation method that allows one to obtain accurate estimates of a quantity using relatively crude trial functions for the physical behavior. This principle is applied to transducer analysis by coupling a variational principle developed for the driving element (including piezoelectric effects) to one for the shell. The motion of the transducer is, in turn, coupled to a variational principle for the pressure in a fluid medium. The modeling of a class V flextensional ring‐shell projector will be presented in detail. The in‐vacuo resonance frequencies for the piezoelectric ring and spherical shell, as well as the in‐vacuo mode shapes for the driver–shell combination will be compared with existing theory and finite element analyses. Results for a free‐flooded piezoelectric ring and immersed spherical shell will be presented as tests of the variational fluid loading formulation. Admittance calculations and beam patterns for a single element will be compared with experimental...

Flextensional transducer modeling using variational principles