A fractal approach of the sound absorption behaviour of materials. Theoretical and experimental aspects

Abstract

In the materials area there are many theoretical and experimental investigations concerning their sound absorption behaviour, covering a wide range of applications. An alternative approach consists in identifying the ensemble acoustic field-propagation environment with a fractal gives its functionality in the form of structure parameters that is dependent on scale resolution. These fractal parameters can be matched with “classical” ones typical for sound absorption experiments in various materials. The mathematical methodology presented here implies the substitution of a dynamics with constraints on continuous but differentiable curves, in an Euclidian space, with “synchronous” dynamics, free from any constraints, on continuous but non-differentiable curves with various fractal dimensions but on a fractal space (i.e. the geodesics of that space). In a very special representation, the external constraints select the fractal geodesics type. In our study this “type selection” refers to the geodesics tunnel effect of fractal (acoustic) type for which we calculate the reflectance and the transparency of an external fractal barrier. An experimental procedure, using a modified impedance tube technique, to determine the sound absorption coefficients for various composite materials was conducted. The procedure uses an anechoic room and the measured sound absorption coefficients also include the sound transmission. The fractal approach of the acoustic behaviour, through the fractal parameters determined (transparency and reflectance) matched the experimental results, in terms of sound absorption, emphasizing the high degree of generality of the fractal theory in the dynamics of physical processes.