Dispersion and attenuation in thermoelastic multisize particulate composites

This paper deals with the problem of multiple scattering by a random distribution of spherical solid particles in a solid. The material properties of both media are taken as thermoelastic. The radii of the inclusions may be different. The self-consistent method in its variant of the effective medium is used to find the dispersion and attenuation of quasi-elastic, quasi-thermal and shear waves. The single scattering problem required by this technique is solved approximately by means of the Galerkin method applied to an integral equation using the Green function. Numerical results display a characteristic resonance phenomena which appears in the interval where the results are approximately valid, that is, for very long waves down to wavelengths about twice the largest diameter of the spheres. Examples are shown, for composites with two sets of inclusions, which have either a very similar or dissimilar size. Comparisons are made with the elastic counterpart. Among the material properties, the mass density ratio, inclusion to matrix, seems to play an important and simple role. Frequency intervals are distinguished and shown to depend on that ratio, where the attenuation and dispersion of quasi-elastic and P-waves are either very close to each other or not at all. The same applies to shear waves in either composite. The mass density ratio also displays a simple monotonic decreasing behaviour as a function of the frequency at the first attenuation maximum and velocity minimum. These results may be of interest for the nondestructive testing characterization of particulate composites.