The acoustic absorption of a porous structure within a specific frequency range can be tuned by varying its porosity along its thickness. In this work, triply periodic minimal surfaces (TPMS) are employed to generate graded porous structures, where the continuous porosity gradient is controlled by a mathematical function involving geometric parameters. A hybrid homogenization technique, combined with the transfer matrix method (TMM), is used to predict the normal incidence absorption coefficient of the graded TPMS structure. The porosity distribution along the thickness is then optimized using a global search method combined with a local gradient-based solver to maximize acoustic absorption within a target frequency range. The optimization results suggest that a combination of high- and low-porosity layers achieves broadband impedance matching conditions by shifting the so-called quarter-wavelength resonance frequencies. The design of the TPMS absorbers is validated through impedance tube measurements of 3D-printed samples.

Triply periodic minimal surfaces (TPMS), a class of periodic implicit surface with zero mean curvature, are emerging as an excellent solution to create graded porous structures. The grading of a porous layer can enhance and broaden the acoustic absorption in a target frequency range. The porosity gradient within the TPMS structure can be precisely controlled by a mathematical function, straightforwardly allowing for optimization towards the desired absorption. As the first step of the optimization procedure, we present a computational approach to determine acoustic absorption properties of functionally graded TPMS porous structures: the transport parameters of a rigid-frame homogeneous TPMS porous absorber are found by the finite element simulations of three static problems, then the absorption coefficient of the TPMS porous structure with graded porosity along the thickness is calculated with the transfer matrix method. The presented approach is validated by direct numerical simula- tions of the same porous structure.