### ASA 124th Meeting New Orleans 1992 October

## 1aEA8. Flextensional transducer modeling using variational principles.

**Harold C. Robinson
**

**
Roger T. Richards
**

**
John B. Blottman, III
**

**
**
*Naval Undersea Warfare Ctr., New London Detachment, New London, CT 06320
*

*
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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 data, equivalent circuit, and finite element analyses. The
extension of the variational method to array interaction modeling will also be
discussed.