Propagation of elastic waves in correlated dispersions of resonant scatterers.

The propagation of coherent longitudinal and transverse waves in random distributions of spherical scatterers embedded in an elastic matrix is studied. The investigated frequency range is the vicinity of the resonance frequencies of the translational and rotational motion of the spheres forced by the waves, where strong dispersion and attenuation are predicted. A technique for making samples made of layers of carbide tungsten beads embedded in epoxy resin is presented, which allows control of the scatterers distribution, induce short-range positional correlations, and minimize the anisotropy of samples. Comparison between phase velocity and attenuation measurements and a model based on multiple scattering theory (MST) shows that bulk effective properties accurately described by MST are obtained from three beads layers. Besides, short-range correlations amplify the effect of mechanical resonances on the propagation of longitudinal and transverse coherent waves. As a practical consequence, the use of short-range positional correlations may be used to enhance the attenuation of elastic waves by disordered, locally resonant, elastic metamaterials, and MST globally correctly predicts the effect of short-range positional order on their effective properties.

Propagation of coherent shear waves in scattering elastic media.

We measure the reflection and transmission of shear waves by slabs of random dispersions of hard, dense spheres in a viscoelastic matrix. By modeling the slab as a Fabry-Pérot interferometer, we determine the effective wave number of coherent shear waves in this scattering medium and its effective mass density. We evidence the effect of the resonant rigid-body translation and rotation of the spheres on the propagation. We validate a vectorial model of multiple scattering for volume fractions of spheres up to 10%, revealing the signature of two modes of propagation.

Viscoelastic shear modulus measurement of thin materials by interferometry at ultrasonic frequencies.

This paper presents a technique for measuring the complex shear modulus of thin slabs of viscoelastic solids based on the measurement of the reflection and transmission of plane shear waves through a sample inserted between two delays lines. Reproducible shear wave transmission through the sample is achieved by inserting bond layers with controlled thickness between the delay lines and the sample and by characterizing beforehand the bond rheology. The frequency dependent complex shear modulus is quantitatively evaluated from the transmission and reflection coefficients using an exact model of interferences within the delay line-bond-sample-bond-delay line sandwich and by selecting the solution among the muliple solutions of the inverse problem from considerations on time of flight and sample thickness. Thanks to its reproducibility and accuracy, this method appears as an original and efficient technique for quantitatively characterizing the high frequency shear modulus of attenuating materials.