Olivier Doutres

Effect of the microstructure closed pore content on the acoustic behavior of polyurethane foams

The present paper proposes to investigate the links between the microstructure of polyurethane foams and their sound absorbing efficiency, and more specifically the effect of membranes closing the cells. This study is based on the complete characterization of 15 polyurethane foam with various cell sizes and reticulation rates (i.e., open pore content): (i) characterization of the microstructure properties (cell size Cs, strut thickness t, reticulation rate Rw…) from SEM pictures, (ii) characterization of nonacoustic parameters (porosity Φ, airflow resistivity σ, tortuosity α∞…) from direct and indirect methods. Existing analytical links between microstructure properties and nonacoustic parameters are first applied to fully reticulated materials. Then, they are improved empirically to account for the presence of the closed pore content. The proposed expressions associated to the Johnson-Champoux-Allard porous model allow a good estimation of the sound absorbing behavior of all polyurethane foams, fully ret...

Evaluation of the acoustic and non-acoustic properties of sound absorbing materials using a three-microphone impedance tube

This paper presents a straightforward application of an indirect method based on a three-microphone impedance tube setup to determine the non-acoustic properties of a sound absorbing porous material. First, a three-microphone impedance tube technique is used to measure some acoustic properties of the material (i.e., sound absorption coefficient, sound transmission loss, effective density and effective bulk modulus) regarded here as an equivalent fluid. Second, an indirect characterization allows one to extract its non-acoustic properties (i.e., static airflow resistivity, tortuosity, viscous and thermal characteristic lengths) from the measured effective properties and the material open porosity. The procedure is applied to four different sound absorbing materials and results of the characterization are compared with existing direct and inverse methods. Predictions of the acoustic behavior using an equivalent fluid model and the found non-acoustic properties are in good agreement with impedance tube measurements.

Validity of the limp model for porous materials: A criterion based on the Biot theory

The validity of using the limp model for porous materials is addressed in this paper. The limp model is derived from the poroelastic Biot model assuming that the frame has no bulk stiffness. Being an equivalent fluid model accounting for the motion of the frame, it has fewer limitations than the usual equivalent fluid model assuming a rigid frame. A criterion is proposed to identify the porous materials for which the limp model can be used. It relies on a new parameter, the frame stiffness influence (FSI), based on porous material properties. The critical values of FSI under which the limp model can be used are determined using a one-dimensional analytical modeling for two boundary sets: absorption of a porous layer backed by a rigid wall and radiation of a vibrating plate covered by a porous layer. Compared with other criteria, the criterion associated with FSI provides information in a wider frequency range and can be used for configurations that include vibrating plates.

A semi-phenomenological model to predict the acoustic behavior of fully and partially reticulated polyurethane foams

This paper proposes simple semi-phenomenological models to predict the sound absorption efficiency of highly porous polyurethane foams from microstructure characterization. In a previous paper [J. Appl. Phys. 110, 064901 (2011)], the authors presented a 3-parameter semi-phenomenological model linking the microstructure properties of fully and partially reticulated isotropic polyurethane foams (i.e., strut length l, strut thickness t, and reticulation rate Rw) to the macroscopic non-acoustic parameters involved in the classical Johnson-Champoux-Allard model (i.e., porosity ϕ, airflow resistivity σ, tortuosity α∝, viscous Λ, and thermal Λ′ characteristic lengths). The model was based on existing scaling laws, validated for fully reticulated polyurethane foams, and improved using both geometrical and empirical approaches to account for the presence of membrane closing the pores. This 3-parameter model is applied to six polyurethane foams in this paper and is found highly sensitive to the microstructure chara...

Complement to standard method for measuring normal incidence sound transmission loss with three microphones

Complement to standard E2611-09 of the American Society for Testing and Materials [Standard Test Method for Measurement of Normal Incidence Sound Transmission of Acoustical Materials Based on the Transfer Matrix Method (American Society for Testing and Materials, New York, 2009)] is proposed in order to measure normal incidence sound transmission loss of materials in a modified impedance tube using a three-microphone two-load or one-load method. The modified tube is a standard two-microphone impedance tube, where a third microphone is mounted on a movable hard termination. This method is conceptually identical to the four-microphone two-load or one-load method described in the standard; however, it requires fewer transfer functions and one microphone less. The method is validated on (1) symmetrical homogeneous and (2) non-symmetrical non-homogeneous specimens.

Impact of the irregular microgeometry of polyurethane foam on the macroscopic acoustic behavior predicted by a unit-cell model

This paper deals with the prediction of the macroscopic sound absorption behavior of highly porous polyurethane foams using two unit-cell microstructure-based models recently developed by Doutres, Atalla, and Dong [J. Appl. Phys. 110, 064901 (2011); J. Appl. Phys. 113, 054901 (2013)]. In these models, the porous material is idealized as a packing of a tetrakaidecahedra unit-cell representative of the disordered network that constitutes the porous frame. The non-acoustic parameters involved in the classical Johnson-Champoux-Allard model (i.e., porosity, airflow resistivity, tortuosity, etc.) are derived from characteristic properties of the unit-cell and semi-empirical relationships. A global sensitivity analysis is performed on these two models in order to investigate how the variability associated with the measured unit-cell characteristics affects the models outputs. This allows identification of the possible limitations of a unit-cell micro-macro approach due to microstructure irregularity. The sensitivity analysis mainly shows that for moderately and highly reticulated polyurethane foams, the strut length parameter is the key parameter since it greatly impacts three important non-acoustic parameters and causes large uncertainty on the sound absorption coefficient even if its measurement variability is moderate. For foams with a slight inhomogeneity and anisotropy, a micro-macro model associated to cell size measurements should be preferred.

Low-frequency absorption using a two-layer system with active control of input impedance

Broadband noise absorption, including low frequencies, may be obtained by a hybrid passive-active two-layer system. A porous layer in front of an air layer provides passive absorption, at medium and high frequencies. Active control of the input impedance of the two-layer system yields absorption at low frequencies. The active control system can implement either pressure-release or impedance-matching conditions. A simple analytical model based upon plane waves propagating in a tube permits the comparison of both control strategies. The results of this simple model show that the pressure-release condition affords higher absorption than the impedance-matching condition for some combinations of geometrical and material parameters. Experimental results corroborate the good performance of the pressure-release condition under the prescribed geometrical setup.

Porous layer impedance applied to a moving wall: Application to the radiation of a covered piston

Modeling a porous layer mounted on a vibrating structure using acoustic impedance is investigated in this paper. It is shown that the use of surface impedance usually measured with the impedance tube method can provide an inaccurate estimation of the acoustic pressure radiated by the covered structure. The paper focuses on the derivation of an impedance, denoted the “transfer impedance,” which describes accurately the dynamic movement of the porous layer. Biot’s theory is used in the model to account for deformations in the thickness of the layer. Experimental validation is performed using a circular piston covered by a foam or a fibrous layer, radiating in an infinite half space. The radiation model including the transfer impedance shows close agreement with experimental data.

On the use of a loudspeaker for measuring the viscoelastic properties of sound absorbing materials

This paper investigates the feasibility to use an electrodynamic loudspeaker to determine viscoelastic properties of sound-absorbing materials in the audible frequency range. The loudspeaker compresses the porous sample in a cavity, and a measurement of its electrical impedance allows one to determine the mechanical impedance of the sample: no additional sensors are required. Viscoelastic properties of the material are then estimated by inverting a 1D Biot model. The method is applied to two sound-absorbing materials (glass wool and polymer foam). Results are in good agreement with the classical compression quasistatic method.

Ironless transducer for measuring the mechanical properties of porous materials

This paper presents a measurement setup for determining the mechanical properties of porous materials at low and medium frequencies by extending toward higher frequencies the quasistatic method based on a compression test. Indeed, classical quasistatic methods generally neglect the inertia effect of the porous sample and the coupling between the surrounding fluid and the frame; they are restricted to low frequency range (<100 Hz) or specific sample shape. In the present method, the porous sample is placed in a cavity to avoid a lateral airflow. Then a specific electrodynamic ironless transducer is used to compress the sample. This highly linear transducer is used as actuator and sensor; the mechanical impedance of the porous sample is deduced from the measurement of the electrical impedance of the transducer. The loss factor and the Youngs modulus of the porous material are estimated by inverse method based on the Biots model. Experimental results obtained with a polymer foam show the validity of the method in comparison with quasistatic method. The frequency limit has been extended from 100 Hz to 500 Hz. The sensitivity of each input parameter is estimated in order to point out the limitations of the method.