Prediction of the dynamic effective properties of particle-reinforced composite materials

The prediction behaviors of some coherent plane wave equations for the effective velocities and attenuations of the coherent plane waves propagating through a composite material and for the effective elastic moduli of the composites are studied. The numerical results obtained by Waterman & Truell's, Twersky's and Gubernatis's equations for Glass-Epoxy composites with various volume fractions are compared. It is found that the predictions by both Twersky's and Gubematis's equations underestimate the effective velocities and the effective elastic moduli when compare with the predictions by Waterman & Truell's equation. Furthermore,the deviations are more evident for the shear wave than that for the longitudinal wave. But these deviations decrease gradually with the increase of the frequency and increase gradually with the increase of the volume fraction.