An acoustic superposition method for computing structural radiation in spatially digitized domains

This paper presents a new method for computing acoustic fields of structural radiators based on acoustic superposition methods using meshless, spatially digitized domains (ASMDD). Here the system matrices are assembled knowing only coordinate points in 3D space that describe the geometry of the radiating structure. In contrast to conventional methods, ASMDD does not require numerical, high orders of integration over elemental surfaces to populate system matrices. The system's Green functions are computed simply between source and receiver locations at their respective points. A new derivation provides an analytical solution for coincident source and receiver points where the Green function is singular. The digital domain of ASMDD is a uniform distribution of points equidistant in the x, y, and z directions. The centroid of each activated voxel (used only as a means for visualizing the 3D surface) represents a point on the structural surface being modeled. Work in this paper exploits the inherent uniformity of neighboring points to formulate a locally determined outward-pointing, surface normal needed for acoustic radiation problems. The ability of the calculated surface normals to model the curvature of the continuous radiating surface depends on the density of the meshless grid, i.e., higher curvature requires higher grid densities. The attractiveness of the digital domain approach is its simplicity for morphing of structural shapes in optimization. Shape iterations in the digitized space reduce to a simple process of activating or deactivating selected points in a contiguous manner depending on the desired shape during an optimization. As an example, the ASMDD formulation is used to compute the modal radiation from a square plate in an infinite and cubic baffle. The ASMDD surface points are shown to blend seamlessly with the surface vibration results of the plate generated via meshless structural dynamics (Meshless Local Petrov Galerkin method - MLPG). This is achieved by solving the modal radiated acoustic power from the plate where the surface velocity is specified by the modal results determined by the MLPG method. The sound power calculations are in good agreement with those generated via conventional BEM codes.