Radiation from an Array of Transducers on a Finite Cylinder

Abstract

It is difficult to obtain valid solutions for a large finite cylindrical array using the Helmholtz integral or source-density formulations because of the density of the eigenfrequencies of the interior of the body. Near these eigenfrequencies, it is difficult to obtain valid solutions. If a hole is drilled through the cylinder, the interior eigenfrequencies of the resulting finite annular cylinder can easily be found. If the hole is large enough so that the resulting wall thickness is less than a half wavelength, then there will be no eigenfrequencies below the sonar frequency and the eigenfrequency problem is avoided. An example is given showing that this hole has negligible effects on the radiated pattern. Beam patterns for an array of six bands on a finite annular cylinder three wavelengths high, 10 wavelengths in diameter, and 14 wavelength in wall thickness are compared with patterns for the same array on an infinite cylinder, for various depression angles. The finite and infinite cylinder patterns looked much alike, with diffraction oscillations added. The diffraction oscillations were seen on the main lobe only for depression angles deeper than 30°.