A variational principle for sound radiation from vibrating bodies

A variational principle governing the acoustic pressure on the exterior of an arbitrary body is derived from the Kirchhoff Helmholtz integral relation. The principle is valid for acoustic radiation and diffraction problems. The general principle is specialized to the case of a thin body and then illustrated by an example of sound radiation from a flat, rigid, circular disk in transverse oscillation. The variational formulation has the surface pressure as the unknown variable, with the velocity normal to the surface taken as given. The Rayleigh Ritz method is used to determine a solution in terms of truncated expansions of basis functions. The basis functions employed are polynomial and trigonometric functions, and piecewise linear functions leading to a finite element description. The results compare very well with previous analytical investigations.