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 purpose of this work is to check if additive manufacturing technologies are suitable for reproducing porous samples designed for sound absorption. The work is an inter-laboratory test, in which the production of samples and their acoustic measurements are carried out independently by different laboratories, sharing only the same geometry codes describing agreed periodic cellular designs. Different additive manufacturing technologies and equipment are used to make samples. Although most of the results obtained from measurements performed on samples with the same cellular design are very close, it is shown that some discrepancies are due to shape and surface imperfections, or microporosity, induced by the manufacturing process. The proposed periodic cellular designs can be easily reproduced and are suitable for further benchmarking of additive manufacturing techniques for rapid prototyping of acoustic materials and metamaterials.

porous materials, designed periodicity, additive manufacturing, sound absorption

Active sandwich panels are an example of smart noise attenuators and a realization of hybrid active-passive approach for the problem of broadband noise reduction. The panels are composed of thin elastic faceplates linked by the core of a lightweight absorbent material of high porosity. Moreover, they are active, so piezoelectric actuators in the form of thin patches are fixed to their faceplates. Therefore, the passive absorbent properties of porous core, effective at high and medium frequencies, can be combined with the active vibroacoustic reduction necessary in a low frequency range. Important convergence issues for fully coupled finite-element modeling of such panels are investigated on a model of a disk-shaped panel under a uniform acoustic load by plane harmonic waves, with respect to the important parameter of the total reduction of acoustic transmission. Various physical phenomena are considered, namely, the wave propagation in a porous medium, the vibrations of elastic plate and the piezoelectric behavior of actuators, the acoustics-structure interaction and the wave propagation in a fluid. The modeling of porous core requires the usage of the advanced biphasic model of poroelasticity, because the vibrations of the skeleton of porous core cannot be neglected; they are in fact induced by the vibrations of the faceplates. Finally, optimal voltage amplitudes for the electric signals used in active reduction, with respect to the relative size of the piezoelectric actuator, are computed in some lower-to-medium frequency range.

Active sandwich panels, Multiphysics, Vibroacoustics, Poroelasticity, Piezoelectricity

This paper presents a complete finite-element description of a hybrid passive/active sound package concept for acoustic insulation. The sandwich created includes a poroelastic core and piezoelectric patches to ensure high panel performance over the medium/high and low frequencies, respectively. All layers are modelled thanks to a Comsol environment*. The piezoelectric/elastic and poroelastic/elastic coupling are fully considered. The study highlights the reliability of the model by comparing results with those obtained from the Ansys finite-element software and with analytical developments. The chosen shape functions and mesh convergence rate for each layer are discussed in terms of dynamic behaviour. Several layer configurations are then tested, with the aim of designing the panel and its hybrid functionality in an optimal manner. The differences in frequency responses are discussed from a physical perspective. Lastly, an initial experimental test shows the concept to be promising.

Poroelasticity, Piezoelectricity, Finite-element modelling, Acoustic insulation, Active-passive approach

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

L’objectif de cette étude est de modéliser et de caractériser le comportement de matériaux réalisés en impression 3D lorsqu’ils sont placés en paroi d’un conduit. Le matériau considéré présente une structure périodique dont la cellule de base comporte une sphère reliée aux sphères des autres cellules par des canaux cylindriques. Le squelette rigide du matériau permet de le modéliser comme un Fluide Équivalent. Quand le matériau est placé en paroi de conduit, la modélisation par son impédance de surface n’est plus suffisante et la propagation dans le matériau doit être prise en compte. Trois modélisations du matériau sont étudiées. Les deux premières s’appuient sur une description macroscopique au moyen d’un Fluide Équivalent. Dans la première, il est décrit par ses fonctions caractéristiques dynamiques (densité et compressibilité), calculées au moyen d’un modèle numérique d’un tube de Kundt. Dans la seconde modélisation, les paramètres du modèle JCALP sont déduits par résolution des équations de Stokes, Laplace et Poisson pour une seule cellule du matériau. Le troisième modèle consiste à décrire le matériau dans sa globalité à l’échelle microscopique et à résoudre les équations de Navier-Stokes Linéarisées (NSL) dans le conduit et le matériau. Les résultats des trois modèles sont comparés en incidence normale et en paroi d’un conduit. Différentes techniques d’impression 3D ont été utilisées pour réaliser des échantillons, et montrent une variabilité importante des géométries effectivement réalisées et par suite des coefficients d’absorption mesurés en tube de Kundt. Les résultats d’expérimentations en paroi de conduit sont également comparés avec ceux de la modélisation.

The paper presents numerical studies of wave propagation under normal and oblique incidence in sound-absorbing layers of poroelastic composites with active and passive inclusions embedded periodically along the composite layer surface. The purpose of active inclusions is to increase the mass-spring effect of passive inclusions attached to the viscoelastic skeleton of the poroelastic matrix of the composite in order to increase the dissipation of the energy of acoustic waves penetrating into such a layer of poroelastic composite. Finite element modelling is applied which includes the coupled models of Biot-Allard poroelasticity (for the poroelastic matrix), piezoelectricity and elastodynamics (for the active and passive inclusions, respectively), as well as the Helmholtz equation for the adjacent layer of air. The formulation based on the Floquet-Bloch theory is applied to allow for modelling of wave propagation at oblique incidence to the surface of the periodic composite layer. The actively exited piezoelectric inclusions may become additional (though secondary) sources for wave propagation. Therefore, a background pressure field in a wide adjacent air layer is used to simulate plane waves propagating from the specified direction, oblique or normal, onto the poroelastic layer surface, and a nonreflecting condition is applied on the external boundary of the air layer.

When airborne acoustic waves penetrate porous media their carrier becomes the air in pores, but also the solid skeleton - provided that it is sufficiently soft. Then, there is a coupled propagation of fluid-borne and solid-borne waves in a poroelastic medium. The coupling of fluid and solid phases of such media can be responsible for significantly better or weaker sound absorption in medium and lower frequency ranges. It has been observed that adding some well-localised small mass inclusions inside a poroelastic layer may improve its acoustic absorption in some medium frequency range, however, at the same time the absorption is usually decreased at some slightly higher frequencies. This situation can be improved by applying additionally an active approach using small piezoelectric inclusions which actively influence the vibrations of the solid skeleton with added masses, so that the interaction between the solid-borne and fluid-borne waves is always directed for a better mutual energy dissipation of the both types of waves.

The paper presents further development in modeling of active elasto-poroelastic sandwich panels. In fact, a new design of a demi-sandwich panel is proposed and analysed. A numerical model of panel is implemented in COMSOL Multiphysics environment using the most fundamental but very flexible Weak Form PDE Mode. Various physical problems are modeled using Finite Element Method: the wave propagation in acoustic and poroelastic medium, the vibrations of elastic plate, the piezoelectric behavior of actuator. All these problems interact. in the examined application of active panel. The presented results of FE analysis and some analytical solutions prove the necessity of modeling the panel's interaction with an acoustic medium. Again, confirmed is the fact that an active control is necessary for lower resonances while for the higher frequencies the passive reduction of vibroacoustic transmission performed by a well-designed poroelastic layer is sufficient.

Active sandiwch panels, Poroelasticity, Piezoelectricity, Vibroacoustics

The paper addresses the issue of an active sandwich panel made of elastic faceplates and a poroelastic core. The panel is supposed to be active thanks to piezoelectric patches glued to the one of elastic layers. This piezoelectric actuator is used to excite the panel vibrations in the low frequency range with the aim to reduce the transmitted wave. A complete description of the sandwich behaviour is obtained using a finite element model implemented in FEMLAB environment. The poroelastic material is modeled using a recent formulation (by Atalla et al.) valid for harmonic oscillations, but the classical Biot formulation is also implemented. Coupling occurring between poroelastic material and plates, and between elastic plate and piezoelectric patches is fully considered. The achieved numerical model allows prediction of transmission coefficient for plane waves under normal incidence. Hence, some numerical experiments can be offered for multiple assembly configurations whose ultimate goal is to determine the best assembly and the best control strategy for reducing the transmission over a wide frequency range.

Poroelacticity, Piezoelectricity, Active vibroacoustic panles