Harold C. Robinson
Elizabeth A. McLaughlin
Naval Undersea Warfare Ctr., New London Detachment, New London, CT 06320
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.]