NUMERICAL IMPLEMENTATION OF THE LUMPED-PARAMETER MODEL FOR THE ACOUSTIC POWER OUTPUT OF A VIBRATING STRUCTURE

In a previous paper, a lumped parameter model for the acoustic radiati on from a vibrating structure was defined by dividing the surface of t he structure into elements, expanding the acoustic held from each of t he elements in a multipole expansion, and truncating all but the lowes t-order terms in the expansion. Here, the lumped parameter model is im plemented numerically by requiring the boundary condition for the norm al surface velocity to be satisfied in a lumped parameter sense. This alleviates the difficulties typically encountered in enforcing the bou ndary condition, leading to a relatively simple numerical solution wit h well-defined convergence properties. The basis functions for the num erical analysis are taken as the acoustic fields of discrete simple, d ipole, and tripole sources located at the geometrical centers of the s urface elements. The different source types are used to represent the radiation from different kinds of surface elements: simple sources for elements in the plane of an infinite baffle, dipole sources for very thin structures which deform only in bending, and tripole sources for elements associated with parts of a structure enclosing a finite volum e. The convergence of the numerical solution for the power output as a function of both frequency and element size is demonstrated through s everal example problems. (C) 1997 Acoustical Society of America.