On broadband absorption in a fractal chirped porous material using a smaller amount of material: Estimates to normal and random incidence.

Designing broadband sound absorption devices using a smaller amount of porous material is of great importance for practical applications: for example, in the civil aviation sector. In this context, this paper proposes a chirped porous material based on the Cantor fractal, and the performance of the absorber is estimated under normal and random wave incidence. For normal incidence and using the transfer matrix method with the Johnson-Champoux-Allard-Lafarge model, and through numerical simulations and experimental tests, this paper demonstrates that the proposed absorber with increasing infinite complexity maintains an average sound absorption (Qα) greater than 90% in a wide frequency range (100-6400 Hz). To achieve these results, the initial generation of the fractal structure must be composed of porous materials with different flow resistivity (σfi), i.e., σf1>σf2. Furthermore, based on the concept of radiation impedance and the first empirical London model, this paper proves that for random incidence, the absorber maintains a behavior similar to that observed for normal incidence up to the second iteration of the structure. Therefore, this study suggests that the Cantor fractal pattern allows the development of broadband sound absorbers that consider a smaller amount of porous material in their design.