_A_ VAKIATIONAL PRINCIPLE FOR SOUND RADIATION YRfM VIBRATING BODIES

COSATI CODES f lELD C«OUP SUB. GR. 1& SUBJECT TERMS tCoHtinua on ravana if naeanary and idanttfy by bioc* numbtr) Acoustics Acoustic Radiation Variational Principle 19. ABSTRACT tContin I lavana if nactuary and idantify by btoek numbar) ABSTRACT 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 isspecialized 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 fxinctions. The basis functions employed'are polynomial and'trigonometric functions, and piece-wise linear functions leading tQ a finite element description. The results compare very well with previous analytical investigations.