On a relative shift in the periodic micro-geometry and other causes for discrepancy in the microstructure-based modelling of 3D-printed porous media

Samples with periodic microstructures, designed for good sound absorption, have been manufactured by 3D printing. Typically, however, the acoustical properties of the resulting samples differ from those predicted. Two causes of the discrepancies are (1) inaccuracies related to the 3D-printing resolution and (2) imperfections resulting from micro-fibres, micro-pores, and pore surface roughness, created during manufacture. Discrepancies due to the first cause can be addressed, post hoc, by updating the idealised periodic geometric model used for creating the codes for fabrication on the basis of a survey using a scanning microscope, or through computerised micro-tomography scans. Reducing the discrepancies due to the second cause requires a relatively significant further modelling effort. Another cause for small discrepancies is when two layers of the same periodic porous material and thickness differ only by a relative shift of the internal geometry of the periodic Representative Volume Element (RVE). This causes the absorption peaks to be shifted in frequency. A modelling procedure is proposed to take this into account.