The effective dynamic moduli and density for composite viscoelastic materials

Abstract

By extending the self‐consistent field technique of Chaban [Sov. Phys.‐Acoust. 10, 298 (1965) and 11, 81 (1965)] we have derived general expressions for the dilatation modulus and density of composite viscoelastic materials. The range of validity extends to values of wavenumber times void radius equal to two, corresponding to the truncation of the partial wave analysis. The effective modulus exhibits resonance behavior in the neighborhood of [k1a] equal to 0.27 for various void volume concentrations and for a range of damping constants. This corresponds quite closely to the resonance that Meyer, Brendel, and Tamm [J. Acoust. Soc. Am. 30, 1116 (1958)] calculated. The moduli exhibit other resonances and stiffness regimes as well. The effective density exhibits sharp double peaks in the region of k1a approximately 0.43 and 0.46 for a range of concentrations and damping constants. For large values of k1a approaching two, the ratio of the effective density to the density of the host material approaches unity. The density, in the long wavelength limit (or static approximation) shows some disagreement with that obtained by Chaban, while the effective moduli in this limit is quite similar to Chaban's to first order.