Estimating the dynamic effective mass density of random composites.

The effective mass density of an inhomogeneous medium is discussed. Random configurations of circular cylindrical scatterers are considered, in various physical contexts: fluid cylinders in another fluid, elastic cylinders in a fluid or in another solid, and movable rigid cylinders in a fluid. In each case, time-harmonic waves are scattered, and an expression for the effective wavenumber due to Linton and Martin [J. Acoust. Soc. Am. 117, 3413-3423 (2005)] is used to derive the effective density in the low frequency limit, correct to second order in the area fraction occupied by the scatterers. Expressions are recovered that agree with either the Ament formula or the effective static mass density, depending upon the physical context.