Directivity patterns of rectangular pistons on prolate spheroids

Abstract

A general expression for the directivity of a rectangular piston arbitrarily located upon a rigid prolate spheroidal baffle is formulated. The piston is assumed to vibrate with uniform normal velocity, and Neumann boundary conditions are imposed in the solution of the problem. The formal solution is expressed in terms of a modal series representation in spheroidal wave functions, valid at any distance from the spheroid. The prolate spheroidal wave functions are obtained using computer programs that have been recently modified and extended to provide accurate values of the wave functions at high frequencies. Substitution of the limiting form of the radial wave functions (as r approaches infinity) into the solution yields the piston far-field single element pattern (SEP). The SEPs for several different piston sizes, orientations, and locations on the spheroidal baffle are presented at various frequencies. [Work supported by ONR Code 321 and Naval Undersea Warfare Center In-house Laboratory Independent Research (ILIR) program.]