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Biot theory [l] is a basic tool when studying the propagation of elastic waves in porous/fibrous solids. Due to the simplicity of the assumptions, isotropic materials are most often utilized [2,3]. However, in some cases, anisotropy has to be included in the modelization, e.g. with some fibrous materials. In this work, we have developped routines, based on the standard Biot model, which compute the various characteristic surfaces (slowness, phase and group velocities) [4] in a given plane for anisotropic porous media. By increasing the weight of the coupling constants, one can continuously vary from the limit case of anisotropic solids with no porosity to a number of different porous media. When the coupling terms are not equal to zero, one finds four instead of three propagating modes, the two other eigenvalues being complex, meaning in turns that the two remaining solutions do correspond to some evanescent modes. The slow transverse mode is unchanged. The fourth mode often called the Biot mode [5], which is very similar to the pseudo-thermal wave [6,7] observed in dynamic thermoelasticity, has always a very small wavespeed and is very highly damped.

This paper provides an analytical solution in the time domain for the propagation of transient ultrasonic waves in a homogeneous, isotropic porous material with a rigid frame. The originality of this propagation equation is the use of the Pride et al. and Lafarge models, which give a better description of acoustic wave attenuation. Two parameters, p and p′, are added to the description of losses in the porous material, given a modification of coefficients of the propagation equation in the time domain. The analytical solution to the wave equation has a different form as compared with that obtained from the Johnson–Allard model. This wave equation contains fractional derivative terms describing attenuation and dispersion in porous material. The Laplace transform method is used to solve the propagation equation. An experimental application to porous plastic foam is given to validate the mathematical solution to the propagation equation.One important result of this work is that the introduction of the two parameters p and p′ corrects the Johnson–Allard model by increasing attenuation with no change in dispersion. This phenomenon is much more significant for resistive porous materials. [Copyright &y& Elsevier]

The aim of this paper is to determine the instantaneous components of a high-speed spinning moving body by means of the pseudo discrete Wigner–Ville distribution (PDWVD). The data access generates an enslaved sampling and, due to the friction forces, the sampling is non-uniform. With respect to sufficient sampling conditions, the PDWVD may be applied in a straight form to the non-uniformily distributed samples. Simulated and real signals are analysed.

A theoretical and experimental study is presented of the aeroelastic instability of the human soft palate, which can explain the occurrence of snoring. The soft palate is modelled by a beam clamped at its leading edge and free at its trailing edge. The continuous and discrete cases are investigated. Only the two first modes of vibration of the soft palate are taken into account. The flow is incompressible, inviscid and one dimensional. Structural damping and flow nonstationarities can be considered. Theory shows that the soft palate loses its stability by flutter and that this instability is mainly controlled by a single dimensionless parameter which can be easily interpreted from a medical point of view. An experimental apparatus which produces sounds very close to human snoring is described. Agreement between theory and experiments is good.

Acoustic propagation in a self-similar porous medium having a rigid frame is studied. A fractional propagation equation in a porous material of non-integer dimension is established using the variational method (Stillinger–Palmer–Stavrinou formalism). The wave equation is solved analytically in the time domain using the Laplace transform method. The analytical solution of the propagation equation shows the existence of a supersonic wave whose front wave velocity depends on the non-integer dimension and the tortuosity of the self-similar porous material. Numerical simulations of the amplitude of the ultrasonic wave inside the material show the sensitivity of the main important parameters describing the propagation (non-integer dimension, tortuosity, viscous and thermal characteristic lengths). The non-integer dimension seems to be the only parameter which acts on both the amplitude and the velocity of the acoustic wave. [ABSTRACT FROM AUTHOR]

This study concerns the acoustic wave diffusion in fractional dimensional rigid porous media in the low frequency domain. An equivalent fluid model with a non-integer dimensional space is developed using the Stillinger–Palmer–Stavrinou formalism. A generalized lossy diffusive equation is derived and solved analytically in the time domain. The coefficients of the diffusion equation are not constant and depend on the fractional dimension, static permeability and porosity of the porous material. The dynamic response of the material is obtained using the Laplace transform method. Numerical simulations of a diffusive wave in porous material with a non-integer dimensional space are given, showing the sensitivity of the waveform to the fractional dimension. It is found that the attenuation of the acoustic wave is more important for the highest value of the fractional dimension d . This result is especially true for resistive porous materials (low permeability value) and for large thicknesses. [ABSTRACT FROM AUTHOR]

This paper provides an analytical solution in the time domain for the propagation of transient ultrasonic waves in a homogeneous isotropic porous material having a rigid frame. The coefficients of the propagation equation are constant and depend only on the acoustical parameters of the porous material. The propagation equation contains fractional derivative terms that describe viscous and thermal interactions between the solid and the fluid. The dynamic response of the material is obtained using the Laplace transform method. An experimental application to porous plastic foams is given to validate the solution of the propagation equation. [Copyright &y& Elsevier]

This paper provides a time domain model for the propagation of transient ultrasonic waves in a self-similar porous material having a rigid frame. This model is based on the formalism of Stillinger–Palmer–Stavrinou, which consists in modeling the fractal material as a porous medium with a non-integer dimensional space. This paper is devoted to the time-domain analytical calculus of the reflection and transmission operators that are expressed in terms of Mittag-Leffler functions. A sensitivity numerical study using ultrasonic reflected and transmitted waves is performed, highlighting the effect of the material's physical parameters (fractal dimension, tortuosity, viscous characteristic length and porosity) on the waveforms. • Ultrasonic propagation in a fractal porous material. • Application of fractional calculus to acoustic propagation in a fractal porous medium. • Modeling the fractal material as a medium with a non-integer dimensional space. • A time-domain modeling of the reflection and transmission operators in terms of Mittag-Leffler functions. [ABSTRACT FROM AUTHOR]