Institute of Fundamental Technological Research

An assembly of additively-manufactured modules to form two-dimensional networks of labyrinthine slits results in a sound absorber with extremely high tortuosity and thereby a relatively low frequency quarter wavelength resonance. Fully analytical modelling is developed for the generic design of such composite acoustic panels, allowing rapid exploration of various specific designs. In addition to labyrinthine channels in a non-porous solid skeleton, a case is also considered where the skeleton has microporosity such that its permeability is very much lower than that due to the labyrinthine channels alone. The analytical modelling is verified by numerical calculations, as well as sound absorption measurements performed on several 3D printed samples of modular composite panels. The experimental validation required overcoming the non-trivial difficulties related to additive manufacturing and testing samples of extreme tortuosity. However, due to the two-dimensionality and modularity of the proposed design, such absorbers can possibly be produced without 3D printing by assembling simple, identical modules produced separately. The experimental results fully confirmed the theoretical predictions that significant sound absorption, almost perfect at the peak, can be achieved at relatively low frequencies using very thin panels, especially those with double porosity.

Sound absorption,Extreme tortuosity,Double porosity,Acoustic composites,Additive manufacturing

The potential usefulness of relatively simple pore microstructures such as parallel, identical, inclined slits for creating broadband sound absorption has been argued through analytical models. In principle, such microstructures could be realised through budget additive manufacturing. However, validation of the analytical predictions through normal incidence impedance tube measurements on finite layers is made difficult by the finite size of the tube. The tube walls curtail the lengths of inclined slits and, as a result, prevent penetration of sound through the layer. As well as demonstrating and modelling this effect, this paper explores two manufacturing solutions. While analytical and numerical predictions correspond well to absorption spectra measured on slits normal to the surface, discrepancies between measured and predicted sound absorption are noticed for perforated and zigzag slit configurations. For perforated microgeometries this is found to be the case with both numerical and analytical modelling based on variable length dead-end pores. Discrepancies are to be expected since the dead-end pore model does not allow for narrow pores in which viscous effects are important. For zigzag slits it is found possible to modify the permeability used in the inclined slit analytical model empirically to obtain reasonable agreement with data.

slitted sound absorber, additive manufacturing, microstructure-based modelling

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.

porous media, periodic microstructure, wave propagation, sound absorption

Understanding the propagation of acoustic waves through a liquid-perfused porous solid frame- work such as cancellous bone is an important pre-requisite to improve the diagnosis of osteoporosis by ultrasound. In order to elucidate the propagation dependence upon the material and structural properties of cancellous bone, several theoretical models have been considered to date, with Biot-based models demonstrating the greatest potential. This paper describes the fundamental basis of these models and reviews their performance.

Acoustic, Propagation, Bone, Theoretical Model

The anisotropic pore structure and elasticity of cancellous bone cause wave speeds and attenuation in cancellous bone to vary with angle. Previously published predictions of the variation in wave speed with angle are reviewed. Predictions that allow tortuosity to be angle dependent but assume isotropic elasticity compare well with available data on wave speeds at large angles but less well for small angles near the normal to the trabeculae. Claims for predictions that only include angle-dependence in elasticity are found to be misleading. Audio-frequency data obtained at audio-frequencies in air-filled bone replicas are used to derive an empirical expression for the angle-and porosity-dependence of tortuosity. Predictions that allow for either angle dependent tortuosity or angle dependent elasticity or both are compared with existing data for all angles and porosities.

The low frequency peaks in the absorption spectra of layers of conventional porous materials correspond to quarter wavelength resonances and the peak frequencies are determined essentially by layer thickness. If the layer cannot be made thicker, the frequency of the peak can be lowered by increasing the tortuosity of the material. Modern additive manufacturing technologies enable exploration of pore network designs that have high tortuosity. This paper reports analytical models for pore structures consisting of geometrically complex labyrinthine networks of narrow slits resembling Greek meander patterns. These networks offer extremely high tortuosity in a non-porous solid skeleton. However, additional enhancement of the low frequency performance results from exploiting the dual porosity pressure diffusion effect by making the skeleton microporous with a significantly lower permeability than the tortuous network of slits. Analytical predictions are in good agreement with measurements made on two samples with the same tortuous slit pattern, but one has an impermeable skeleton 3D printed from a photopolymer resin and the other has a microporous skeleton 3D printed from a gypsum powder.

sound absorption, high tortuosity, dual porosity, 3D printed materials

Low-frequency sound absorption by thin rigid porous hard-backed layers is enhanced if the geometrical tortuosity is increased. Increasing tortuosity increases the fluid flow path length through the porous layer thereby increasing the effective thickness. In turn, this reduces the effective sound speed within the layer and the frequency of the quarter wavelength layer resonance. One way of increasing tortuosity is through rectangular labyrinthine channel perforations. In addition to the tortuosity of the porous matrix, the bulk tortuosity value is influenced by the channel widths, lengths, and number of folds. A sample with an impervious skeleton and a sample in which the solid skeleton is perforated with oblique cylindrical holes evenly spaced in a rectangular pattern have been fabricated using conventional methods and an additive manufacturing technology, respectively. The sound absorption spectra resulting from these structures have been predicted analytically as well as numerically and compared with normal incidence impedance-tube measurements.

Designs with uniformly distributed slits normal or inclined to the incident surface exhibit a great potential because of their simplicity and good acoustical performance. However, production of materials of this sort is challenging as the required fabrication precision is very high. This paper deals with additive manufacturing, modeling, and impedance tube testing of a few slitted geometries and their variations, including cases where the dividing walls between slits are perforated. They were designed to be producible with current 3D printing technology and provide reliable measurements using standardized equipment. The normal incidence sound absorption curves predicted analytically and numerically were verified experimentally. It is observed that such simple configurations may lead to absorption properties comparable to porous acoustic treatments with more complex microstructure. The good agreement between the predictions and measurements supports the validity of the multi-scale modeling employed.

An acoustical characterisation of additively manufactured rigid slitted structures is considered. A set of six JCAL microstructural parameters is deduced from dynamic density and bulk modulus obtained from normal incidence surface acoustic impedance experimental data. The results show that the characteristic lengths are the most difficult to characterise.