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Abstract:
At first glance, it seems that modern, inexpensive additive manufacturing (AM) technologies can be used to produce innovative, efficient acoustic materials with tailored pore morphology. However, on closer inspection, it becomes rather obvious that for now this is only possible for specific solutions, such as relatively thin, but narrow-band sound absorbers. This is mainly due to the relatively poor resolutions available in low-cost AM technologies and devices, which prevents the 3D-printing of pore networks with characteristic dimensions comparable to those found in conventional broadband sound-absorbing materials. Other drawbacks relate to a number of imperfections associated with AM technologies, including porosity or rather microporosity inherent in some of them. This paper shows how the limitations mentioned above can be alleviated by 3D-printing double-porosity structures, where the main pore network can be designed and optimised, while the properties of the intentionally microporous skeleton provide the desired permeability contrast, leading to additional broadband sound energy dissipation due to pressure diffusion. The beneficial effect of additively manufactured double porosity and the phenomena associated with it are rigorously demonstrated and validated in this work, both experimentally and through precise multi-scale modelling, on a comprehensive example that can serve as benchmark.

Keywords:
double porosity, additive manufacturing, sound absorption, pressure diffusion, multi-scale modelling

Abstract:
This work presents benchmark examples related to the modelling of sound absorbing porous media with rigid frame based on the periodic geometry of their microstructures. To this end, rigorous mathematical derivations are recalled to provide all necessary equations, useful relations, and formulae for the so-called direct multi-scale computations, as well as for the hybrid multi-scale calculations based on the numerically determined transport parameters of porous materials. The results of such direct and hybrid multi-scale calculations are not only cross verified, but also confirmed by direct numerical simulations based on the linearised Navier-Stokes-Fourier equations. In addition, relevant theoretical and numerical issues are discussed, and some practical hints are given.

Keywords:
porous media, periodic microstructure, wave propagation, sound absorption

Abstract:
This work discusses many practical and some theoretical aspects concerning modelling and design of plates with micro-slits, involving multi-scale calculations based on microstructure. To this end, useful mathematical reductions are demonstrated, and numerical computations are compared with possible analytical estimations. The numerical and analytical approaches are used to calculate the transport parameters for complex micro-perforated (micro-slotted) plates, which allow to determine the effective properties of the equivalent fluid, so that at the macro-scale level the plate can be treated as a specific layer of acoustic fluid. In that way, the sound absorption of micro-slotted plates backed with air cavities can be determined by solving a multi-layer system of Helmholtz equations. Two such examples are presented in the paper and validated experimentally. The first plate has narrow slits precisely cut out using a traditional technique, while the second plate - with an original micro-perforated pattern - is 3D-printed.

Keywords:
micro-slotted plates, micro-perforated plates, sound absorption, microstructure-based modelling, 3D-printing

Abstract:
Selective laser sintering and binder jetting are two additive manufacturing technologies that use loose powder as a feedstock. In the case of binder jetting, the printout walls are essentially permeable and need to be additionally impregnated to be fully air-tight. The permeability of sintered objects, on the other hand, can be controlled to some extent by the amount of laser energy, among other things, provided to the exposed layer. Exploring these two technologies, several single- and double-porosity samples were additively manufactured, examined and acoustically measured in an impedance tube. Moreover, the normal incidence sound absorption spectra resulting from these structures were predicted employing multi-scale methods. The values of porosity and permeability of permeable printed materials were determined and utilised in the applied modelling. It is observed that making the skeleton microporous and permeable enables effective sound absorption even in primitive 3D printed acoustic treatments.

Abstract:
This paper shows that specific additive manufacturing (AM) technology can be used to produce double-porosity acoustic materials where main pore networks are designed and a useful type of microporosity is obtained as a side effect of the 3D printing process. Here, the designed main pore network is in the form of annular pores set around the axis of the cylindrical absorber. In this way, the axial symmetry of the problem is ensured if only plane wave propagation under normal incidence is considered, which allows for modelling with purely analytical expressions. Moreover, the outermost annular pore is bounded by the wall of the impedance tube used to measure the sound absorption of the material, so that experimental tests can be easily performed. Two different AM technologies and raw materials were used to fabricate axisymmetric absorbers of the same design, in one case obtaining a material with double porosity, which was confirmed by the results of multi-scale calculations validated with acoustic measurements.

Abstract:
The paper shows that acoustic materials with double porosity can be 3D printed with the appropriate design of the main pore network and the contrasted microporous skeleton. The microporous structure is obtained through the use of appropriate additive manufacturing (AM) technology, raw material, and process parameters. The essential properties of the microporous material obtained in this way are investigated experimentally. Two AM technologies are used to 3D print acoustic samples with the same periodic network of main pores: one provides a microporous skeleton leading to double porosity, while the other provides a single-porosity material. The sound absorption for each acoustic material is determined both experimentally using impedance tube measurements and numerically using a multiscale model. The model combines finite element calculations (on periodic representative elementary volumes) with scaling functions and analytical expressions resulting from homogenization. The obtained double-porosity material is shown to exhibit a strong permeability contrast resulting in a pressure diffusion effect, which fundamentally changes the nature of the sound absorption compared to its single-porosity counterpart with an impermeable skeleton. This work opens up interesting perspectives for the use of popular, low-cost AM technologies to produce efficient sound absorbing materials.