Acoustics of Fractal Porous Material and Fractional Calculus

In this paper, we present a fractal (self-similar) model of acoustic propagation in porous material with rigid structure. The medium is modeled as continuous non-integer spatial dimension. basic equations acoustics are written. model, the fluid space considered while solid matrix non-fractal. fluid–structure interactions described by fractional operators time domain. resulting equation contains derivative terms and space-dependent coefficients. wave solved analytically domain, reflection transmission calculated for slab material. Expressions responses (reflection transmission) to an excitation show that it possible deduce these from those obtained non-fractal medium, only replacing thickness effective depending on dimension This result shows us that, thanks dimension, can increase (sometimes ratio 50) decrease equivalent wavefront speed depends admits several supersonic values. These results open scientific challenge creation new materials, such metamaterials very specific properties.