### ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

## 4pEA10. Variational model for the radiation impedance of class IV
transducers.

**Harold C. Robinson
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Elizabeth A. McLaughlin
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*Naval Undersea Warfare Ctr., New London Detachment, New London, CT 06320
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In a previous paper [H. C. Robinson, J. Acoust. Soc. Am. 95, 2833 (A)
(1994)], a variational method for determining the modal radiation impedance of
baffled transducer arrays, based on the radiated power, was presented. In this
paper, these variational methods will be extended to include unbaffled arrays
of radiators with arbitrary spatial orientation. The surface velocity of each
of the radiators is represented by in vacuo eigenmode expansions, while the
surface pressure is given by expansions in suitable trial functions. The
arbitrary orientation of the array elements will be represented by transforming
the surface velocities and pressures using Euler angles. As a specific example,
the case of two coplanar class IV flextensional transducers will be examined in
detail. The in vacuo eigenmodes of a single element will be determined using
finite element methods and parametrized in elliptical cylindrical coordinates
((xi),(eta),z). The surface pressure trial functions will be judiciously chosen
functions of ((xi),(eta),z) as well. The behavior of the modal radiation
impedances as a function of dimensionless separation distance kd, as well as of
relative orientation, will be investigated. Comparisons of the results to
equivalent circuit models and experimental data will be presented. [Work
sponsored by ONR.]