Element Free Structural Acoustics for Efficient Shape Optimization

Abstract

Optimal shape design to acoustically tailor arbitrary radiating structures is one approach to optimal structural acoustic design that has not been extensively employed due to the added complexities inherent in the grid remeshing requirements. In the research described in this paper, the acoustic superposition method is used to determine the sound power radiation objective function and relies on prescribed virtual acoustic sources to match the structural surface volume velocity. The acoustic surface pressure over each element of the discretized model is then determined via straightforward matrix multiplication. Finally, the sound power radiated can be written in terms of a set of constant independent structural basis vectors each being modified by a dependent modal participation factor. However, using structural geometry as a design variable requires that the structural volume velocity be expanded using a new set of basis vectors upon each iteration. As such, the Raleigh-Ritz Method of determining modal participation factors which modify predetermined structural basis vectors cannot be used as this original set of basis vectors has changed with the geometry iteration. Therefore, the acoustic superposition elements must be numerically revaluated for each design iteration converging to meet the objective function. This results in a computationally intensive method that degrades design efficiency. Furthermore, the possibility of element distortion must be efficiently monitored and corrected if necessary during shape movements which further complicate the optimization. As such, a new meshless acoustic method is being developed that removes the need for the costly element by element integration of traditional boundary element analysis and relies only on matrix operations to evaluate the objective function. This results in rendering shape optimization more efficient in optimal structural acoustic design. To demonstrate, using a model of a simple radiation problem, it will be shown that numerical instabilities such as singularities and nonuniqueness problems can be avoided using meshless acoustics.