Low-Frequency Sound Radiation from Slender Bodies of Revolution

Abstract

The radiated pressure field due to the low-frequency vibration of a slender body of revolution is expressed in terms of a distribution of sources and doublets along the body axis. The strength of the singularities is determined from an analysis of the flow near the slender body. For axially symmetric flow, a longitudinal rigid-body vibration and a simple type of accordion vibration are considered. For these examples, the source distribution has the dominant effect on the farfield pressure. For transverse vibration, there is only a doublet distribution. The strength of the doublet distribution depends on the force that the body exerts on the fluid. For wavelengths much greater than the maximum body diameter, this force can be conveniently determined by the extended Lagally theorem of incompressible hydrodynamics. Formulas for the farfield pressure for each type of vibration are given for spheroids and a simple class of streamlined bodies. Examples illustrating the effect of change in body shape and type of vibration are given.