Radiation of Acoustic Energy from a Long Rod into a Semi-Infinite Liquid Medium

Abstract

The solution of the problem of the semi-infinite cylindrical ideal rod set in an infinite baffle and radiating into a semi-infinite ideal liquid is the subject of this paper. An approximation method is utilized. The axisymmetric stress fields in the rod are expressed as infinite sums over eigenvalues which are solutions of the dispersion equation. The dispersion equation is obtained by satisfying the appropriate boundry conditions for the rod. The pressure in the liquid is derived using the Green's functions technique. An infinite series of integrals is the result, since the velocity of the rod must be inserted in the integral expression for pressure. In order to solve the problem numerically these infinite sums are truncated. By matching the boundary conditions across the interface, the velocity profile is obtained which can then be used to construct the farfield radiation patterns in the liquid. Power, radiation impedance, beamwidth, directivity factor, and the directivity index are calculated from the fields. The computer results obtained over a limited frequency range for the aluminum-water case validate the approximation method. The technique provides a general method for calculating the velocity profile at the boundary between a vibrating cylindrical rod and a semi-infinite medium.