Dispersion of elastic waves in random particulate composites

Elastic wave propagation in a discrete random medium is studied to predict dynamic effective properties of composite materials containing spherical inclusions. A self‐consistent method is proposed which is analogous to the well‐known coherent potential approximation in alloy physics. Three conditions are derived that should be satisfied by two effective elastic moduli and effective density. The derived self‐consistency conditions have the physical meaning that the scattering of a coherent wave by the constituents in the effective medium vanishes, on the average. The frequency‐dependent effective wave speed and coherent attenuation can be obtained by solving the self‐consistency conditions numerically. At the lowest resonance frequency, the phase speed increases rapidly and the attenuation reaches the maximum in the composites having a large density mismatch. The lowest resonance is caused mainly by the density mismatch between matrix and particles and higher resonances by the stiffness mismatch. The dispersion and attenuation of longitudinal and shear waves are affected by the lowest resonance much more than by higher ones. The lowest resonance frequency of particles in the effective medium is found to be higher than that of a single particle embedded in the matrix material of composites due to the stiffening effect. The results obtained from the present theory are shown to be in good agreement with previous experimental observations of Kinra et al. [Int. J. Solid Struct. 16, 301–312 (1980)]. Part of the calculated results are compared with those computed by the Waterman and Truell theory. The present theory is in better agreement with the experiments for the examples dealt with.