Jean-Michel Génevaux

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.

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.

A Frequency Independent Criterion for Describing Sound Absorbing Materials by a Limp Frame Model

This paper proposes a criterion to determine if an absorbing porous material can be modeled with the ”equivalent fluid” limp model instead of Biot model. The limp model is derived from Biot theory assuming that the porous frame has no bulk stiffness. The proposed criterion offers a practical simplification of the frequency dependent criterion defined previously by the authors: it depends only on the bulk modulus of the frame and on its porosity. Frequency independent critical values, below which the effect of the frame stiffness can be neglected, are determined for the whole considered frequency range [1 − 10 000 Hz]. The critical values are gathered in charts for different porous thicknesses and two configurations: sound absorption of a porous layer backed by a rigid backing and sound radiation of a plate covered by a porous layer. Its is shown that the derived criterion matches Beranek criterion but it is less restrictive.

Acoustic radiation of a vibrating wall covered by a porous layer: Transfer impedance concept and effect of compression

The acoustic radiation of a vibrating wall covered by a porous layer is investigated. The porous layer is described by the one‐dimensional Biot model: it accounts for the propagation of the two longitudinal waves in the porous layer within its thickness. The transfer impedance concept [Doutres et al., J. Acoust. Soc. Am. 121, 206–213 (2007)] allows to determine the effect of the porous layer on the acoustic radiation of the vibrating wall. This impedance differs from the surface impedance that can be measured in a plane wave impedance tube. It is shown that the radiation efficiency of the structure increases in the vicinity of the first resonance of the skeleton in its thickness and decreases for higher frequencies. Experimental validation is performed with a baffled piston covered by a foam or a fibrous layer. Only the radiation model using the transfer impedance shows close agreement with experimental data. Finally, effect of compression of the porous layer is investigated by both analytical and experim...

Validity of the One-Dimensional Limp Model for Porous Media

A straightforward criterion for determining the validity ofthe limp model validity for porous materials is addressed here. The limp model is an “equivalent fluid” model which gives a better description of porous behavior than the well known “rigid frame” model. It is derived from the poroelastic Biot model, assuming that the frame has no bulk stiffness. A criterion is proposed for identifying 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 1D analytical modeling for a specific boundary set: radiation of a vibrating plate covered by a porous layer.