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

by Zellers, Brian C.

This thesis 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 cumbersome numerical, high orders of integration over elemental surfaces to populate system matrices. The system’s Greens functions are computed simply between source and receiver locations at their respective points. A new derivation presented in this work provides an analytical solution for coincident source and receiver points where the Greens function is singular. Because of the simplifications used in the ASMDD method, the matrix formulation routines are highly efficient. A significant contribution of this thesis is the rendering of ASMDD point-based structures in a digital computational domain. The digital domain 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 thesis 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. Shape iterations in the digitized space reduces 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 of this, the ASMDD formulation is used to compute the radiation from a square piston in a cubic baffle. In the first example, the square piston shape is morphed to a hemi-sphere through five evolutionary changes in shape. The sound power calculations are in good agreement with those computed with conventional BEM codes for shape changes that have low changes in curvature. For a second iv example, the ASMDD surface points are shown to blend seamlessly with surface vibration 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 again in good agreement with those generated via conventional BEM codes. v