Francine Luppé

Scattering by a fluid cylinder in a porous medium: Application to trabecular bone

In a trabecular bone, considered as a nondissipative porous medium, the scattering of an incident wave by cylindrical pores larger than the wavelength is studied. The goal is to know if scattering alone may cause such a high attenuation as that observed in calcaneus. The porous medium is modelized via Biots theory and the scattering by a single pore is characterized from the definition of a scattering matrix. An approximation of weakly disordered medium is then discussed to estimate the effective attenuation and dispersion as a function of frequency. These effective properties are shown to be different of those measured on calcaneus, due to the neglect of wave conversions during the scattering process.

Reflection and transmission by randomly spaced elastic cylinders in a fluid slab-like region

An extension of Fikioris and Waterman’s formalism is developed in order to describe both the reflection and transmission from a slab-like fluid region in which elastic cylindrical scatterers are randomly placed. The dispersion equation of the coherent wave inside the slab must be solved numerically. For solid cylinders, there is only one solution corresponding to a mean free path of the coherent wave larger than one wavelength. In that case, the slab region may be described as an effective dissipative fluid medium, and its reflection and transmission coefficients may be formally written as those of a fluid plate. For thin hollow shells, a second solution of the dispersion equation is found, at concentrations large enough for the shells to be coupled via the radiation of a circumferential Scholte–Stoneley A wave on each shell. This occurs at a few resonance frequencies of the shells. At those frequencies, then, two different coherent waves propagate in the slab, and it can no longer be considered a dissipa...

Effective wave numbers for thermo-viscoelastic media containing random configurations of spherical scatterers

The dispersion relation is derived for the coherent waves in fluid or elastic media supporting viscous and thermal effects and containing randomly distributed spherical scatterers. The formula obtained is the generalization of Lloyd and Berrys [Proc. Phys. Soc. London 91, 678-688 (1967)], the latter being limited to fluid host media, and it is the three-dimensional counterpart of that derived by Conoir and Norris [Wave Motion 47, 183-197 (2010)] for cylindrical scatterers in an elastic host medium.

N-shell cluster in water: Multiple scattering and splitting of resonances

Clusters of N thin parallel and identical shells (aligned or not) in water are considered. Assuming a harmonic plane wave is normally incident upon one cluster, the scattered-field classical expression is recalled, and then computed for different types of clusters, along with resonance spectra. The scattering S matrix is defined, and its unitarity property used to check the numerical results. All spectra are compared with that of a single shell, in the frequency range where resonances are due to an A-wave phase matching only. Whatever the cluster, each resonance of the single shell is seen to split into M different ones. The value of M depends on the number of shells, the distance between them, and the symmetries of the cluster. Apart from the very special case of aligned shells (M=2N), no simple law has been found to predict the value of M.

Normal modes of a poroelastic plate and their relation to the reflection and transmission coefficients.

A poroelastic plate that obeys the Biot theory is considered. Compact new forms of its reflection and transmission coefficients, similar to those of the resonance scattering theory for an elastic plate, are derived. A numerical comparison of the reflection coefficient modulus with the plate normal modes, at low frequency, shows that a study of the reflection or transmission coefficient does not provide the same kind of information on the poroelastic plate than an investigation of guided leaky waves propagation.

Multiple scattering in a trabecular bone: Influence of the marrow viscosity on the effective properties

The Foldy and the Waterman and Truell approximations are used to determine the effective properties of the coherent wave that emerges after multiple scattering of a plane longitudinal fast wave by the largest pores in a trabecular bone. The unit scattering cell considered is either a single pore or two close cylindrical pores (cluster), at a fixed overall bone porosity. In the cluster case, the effective attenuation is about twice that obtained with one single pore per scatterer. It is shown that taking into account the marrow viscosity leads only to minor differences on the effective dispersion and attenuation.

Coherent waves in a multiply scattering poro-elastic medium obeying Biot's theory

Twerskys theory is generalized to multiple scattering by a uniform random distribution of cylinders in a poro-elastic medium. The high-frequency regime only, where no dispersion effects occur in the absence of scatterers, is investigated in the frame of Biots theory. The scatterers lie within a slab of the host medium, and an incident wave gives rise to a fast longitudinal coherent wave, a slow longitudinal one, as well as a shear one in the slab. The dispersion equations of those three coherent waves are derived. The shear coherent wave propagates independently of the other two, while the longitudinal coherent waves obey a coupled dispersion equation involving conversion terms. Numerically speaking, coupling effects are significant only when forward scattering by a single cylinder of the fast wave into the slow one (or the slow wave into the fast) is larger than forward scattering with no conversion.

Experimental study of the Stoneley wave at a plane liquid–solid interface

Some of the properties of the Stoneley wave at a plane liquid–solid interface are reviewed after having deduced them from the general ones of evanescent plane waves. A liquid wedge method of generation of this wave is presented, and the predicted properties are verified.

Observation of surface waves on a solid cylinder in a fluid

An experimental study of the scattering of ultrasonic short pulses by aluminum cylinders in water at grazing incidence for values of ka=50–140 is presented. Surface waves with speed ≲c (sound speed in water) are observed, and their dependence on angular distance traveled over the circumference of the cylinder is measured. In addition to presentation of the measurement of the first Franz‐type surface wave that had been previously observed [W. G. Neubauer, J. Acoust. Soc. Am. 44, 298 (1968); 45, 1134 (1969); Maze et al., Phys. Lett. 75 A, 214 (1980)], evidence of the ultrasonic excitation of the second Franz wave, and possible evidence of the excitation of the Scholte (or Stoneley) wave, is also shown. Of these, the second Franz wave has never been observed before.

Multiple scattering in porous media: comparison with water saturated double porosity media.

Multiple scattering in a poroelastic medium obeying Biots theory is studied; the scatterers are parallel identical cylindrical holes pierced at random in the medium. The paper focuses first on the influence, on the effective wavenumbers, of the mode conversions that occur at each scattering event. The effect of the holes on the dispersion curves is then examined for two different values of the ratio of their radius to the pores mean radius. Depending on the latter, the dispersion curves of the pierced material are compared, for the fast and shear waves, with those of either a more porous medium or a double porosity medium.