Propagation of longitudinal elastic waves in composites with a random set of spherical inclusions (effective field approach)

Abstract

The work is devoted to the problem of plane monochromatic longitudinal wave propagation through a homogeneous elastic medium with a random set of spherical inclusions. The effective field method and quasicrystalline approximation are used for the calculation of the phase velocity and attenuation factor of the mean (coherent) wave field in the composite. The hypotheses of the method reduce the diffraction problem for many inclusions to a diffraction problem for one inclusion and, finally, allow for the derivation of the dispersion equation for the wave vector of the mean wave field in the composite. This dispersion equation serves for all frequencies of the incident field, properties and volume concentrations of inclusions. The long and short wave asymptotics of the solution of the dispersion equation are found in closed analytical forms. Numerical solutions of this equation are constructed in a wide region of frequencies of the incident field that covers long, middle, and short wave regions of propagating waves. The phase velocities and attenuation factors of the mean wave field are calculated for various elastic properties, density, and volume concentrations of the inclusions. Comparisons of the predictions of the method with some experimental data are presented; possible errors of the method are indicated and discussed.

Random acoustic metamaterial with a subwavelength dipolar resonance

“…For the case of randomly distributed elastic spheres in elastic media, explicit models, in which effective wavenumber is given by an explicit formula, 42 and self-consistent models, in which it is the solution of a characteristic equation, 40 have been proposed. In the following, the explicit model derived in Ref.…”

Analysis of the Effective Dynamic Properties of Particulate Composites with Respect to Constituent Properties

“…He showed that, for dense composites, the model performed better than the mean-field methods. In addition, Kanaun and Levin (2007) used the effective field and medium approaches to derive the equations describing elastic wave scattering through such composites. Rahimzadeh and Daneshjoo (2014) conducted a comparative study on four different theoretical models for the prediction of propagation behavior of the elastic P-wave in composites reinforced by randomly distributed inclusions.…”

A simplified metaelastic model for coated sphere-filled random composites

“…However, most existing analytical works are either limited to 1D illustrative models or involved in rather lengthy mathematical formulations and numerical calculations, and many of them are even largely focused on periodic metaelastic composites (such as ''metaconcretes'' filled with periodically aligned coated stiff spheres [10,[12][13][14]). Indeed, random metaelastic composites filled with randomly distributed local resonators have received much less attention [15][16][17][18]. Therefore, it is of great interest to develop simple analytical models that can be used to analyze general metaelastic dynamic problems of random composites filled with coated stiff spheres.…”