Hilbert Fractal Metamaterials for lightweight sound insulation

Low frequencies sound insulation for aerospace [1] and automotive [2] applications is difficult to deal with effectively using material layers with low density and low thicknesses. Traditional approaches for solving this problem are limited by space and weight constraints. A new approach is needed to achieve the desired acoustic performance with a lower volume and weight, hereby tackling fuel consumption in this way [3]: the use of metamaterials in acoustics applications is a potential solution [4]. This work is focused on the effects of Hilbert Fractal Metamaterials (HFM) on acoustics waves. The cavities have geometries that obey mathematical formulae covering zero to fifth order scales, as well as geometrical equivalents which are not fractals. Samples were manufactured by 3D printing and tested for acoustic interactions in an impedance tube. The goal of this work was to evaluate the feasibility of the concept and to design a tool to guide the use of metamaterials in the field of acoustics. The experimental work was performed using a Design of Experiments (DoE) approach, with combinations of design factors and levels of acoustic response being considered to identify the interaction amongst independent variables of the metamaterial structure. The experimental results have led to the creation of a performance map that can be used by engineers to make informed decisions to achieve acoustic insulation with metamaterials.