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This paper proposes an alternative displacement formulation of Biot’s linear model for poroelastic materials. Its advantage is a simplification of the formalism without making any additional assumptions. The main difference between the method proposed in this paper and the original one is the choice of the generalized coordinates. In the present approach, the generalized coordinates are chosen in order to simplify the expression of the strain energy, which is expressed as the sum of two decoupled terms. Hence, new equations of motion are obtained whose elastic forces are decoupled. The simplification of the formalism is extended to Biot and Willis thought experiments, and simpler expressions of the parameters of the three Biot waves are also provided. A rigorous derivation of equivalent and limp models is then proposed. It is finally shown that, for the particular case of sound-absorbing materials, additional simplifications of the formalism can be obtained. [ABSTRACT FROM AUTHOR]

This study deals with sound propagation in typical traffic noise conditions. The numerical results are obtained through the split-step Padé method and the discrete random Fourier modes technique. These are first evaluated qualitatively, by color contour maps showing noise propagation, diffraction by an impedance discontinuity or a screen edge, and scattering by atmospheric turbulence. Next, our numerical results are quantitatively validated by comparison with analytical models and other parabolic equation models. For all the atmospheric conditions and geometrical configurations available in literature, the agreement between the different methods is very good, except for some cases involving the atmospheric turbulence. However, in those particular cases, the split-step Padé results are shown to be more consistent with physical theory. Finally, our method seems to be very powerful and reliable for traffic noise prediction. © 2002 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

A method is presented that allows the prediction of the acoustical properties of layered porous or fibrous materials in normal incidence from simple measurements. Transfer matrices obtained from the Biot theory are used to describe homogeneous layers and screens constituting layered materials. The description of an absorbing material with the method is given. [ABSTRACT FROM AUTHOR]

A new method for measuring impedance has been used for evaluating the normal surface impedance of three foams in free field. The results have been interpreted using the Biot theory, the two dilatational waves being taken into account. It has been pointed out from the theory that, for high flow resistance, the ratio of the acoustical velocities of the frame and the air is close to 1 at the surface of the foam. This ratio decreases with flow resistance but is never negligible for the studied foams. For foams with high flow resistance, the contributions of the two waves must be taken into account when calculating the impedance, and a description with only one wave would not be realistic. For foams with medium flow resistance, the one-wave approximation for calculating the surface impedance is a good approximation in the whole range of acoustical frequencies. [ABSTRACT FROM AUTHOR]

A matrix representation of the acoustical properties of porous layers at oblique incidence is used to predict the surface impedance of layered porous materials with impervious screens. The screens can be located inside the material or at the surface. Comparisons between prediction and measurement achieved with a new technique are given. [ABSTRACT FROM AUTHOR]

The Biot model has been used extensively for the last 30 years. The equations of continuity of the models traditionally used to predict the acoustical properties of sound-absorbing materials are compared here to simplified expressions obtained from the Biot model. From this comparison, it is possible to point out inconsistencies in traditional models. [ABSTRACT FROM AUTHOR]

A fast variation of the surface impedance of two layers of different thicknesses of the same material has been observed at low frequencies. These variations, which are predicted by the Biot theory, appear at the λ/4 resonance of the frame. © 1991 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

Biot has shown that two compressional waves can propagate in a porous material with an elastic frame. For a material with a heavy frame and a medium flow resistivity, one of these waves propagates mainly in air, and the other is created by frame oscillations. The amplitude of this wave, which is generally negligible, can be important at the λ/4 resonance of the frame. A fast variation of the surface impedance appears at this resonance. This effect, which is predictible with the Biot theory, has been observed on a glass wool of high stiffness. [ABSTRACT FROM AUTHOR]