Fractal surfaces: Generation and acoustic scattering prediction.

Abstract

Typical acoustical diffuser design results in diffuse sound scattering only for a limited frequency band, which is problematic given the breadth of the human audible frequency range. Surfaces exhibiting fractal geometries may address this problem due to their self-similarity over multiple scales. Stochastic fractals, such as the random midpoint displacement (RMD) fractal, are well-suited to this usage since they can be mapped onto physical surfaces appropriate for acoustical diffusers. In the current project, virtual RMD fractal surfaces were generated and then constructed using a 3-D printer. A pilot study has been conducted to determine the scattering properties of the fractal surfaces using a numerical prediction scheme carried out using the boundary element method (BEM). Experimental measurements of the scattering properties were also carried out according to ISO 17497. The numerical predictions and experimental measurements were contrasted to improve numerical prediction accuracy and optimize the fractal design parameters of acoustical diffusers. These parameters include surface roughness, fractal dimensionality, number of iterations, and the random number probability distribution function. The comparison of the numerical and experimental results will be presented along with effects of the fractal design parameters.