Harold C. Robinson
Naval Undersea Warfare Ctr., New London Detachment, New London, CT 06320
The variational principle is an approximation method that allows one to obtain accurate estimates of certain quantities 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 surface pressure in a fluid medium. The modeling of a class IV flextensional transducer will be presented in detail. The in vacuo resonance frequencies for the piezoelectric driving stack and elliptical shell, as well as the in vacuo mode shapes for the driver-shell combination will be compared with existing theoretical and finite-element analyses. Variationally determined surface pressures for a single transducer will be presented and compared to finite-element results. Admittance plots and beam patterns for the single element will be shown. [This work was sponsored by the Office of Naval Research.]