Effective mass density of a random configuration of cylinders.

Abstract

The dynamic effective mass density of a random distribution of n0 cylinders/m2 in an ideal fluid is looked for. The Fikioris and Waterman approach is used to obtain the reflection coefficient of the random half‐space at the plane interface with the ideal fluid. This coefficient is expanded into powers of n0, using Linton and Martin’s expansion of the wavenumber of the coherent wave. The reflection coefficient is then compared to that obtained when a homogeneous viscous fluid replaces the random medium. When the two reflection coefficients are equal, the random fluid is acoustically equivalent to the viscous one, which is thus considered as the effective fluid. The coherent wave in the random medium is described as the acoustic mode in the effective fluid, with the shear viscosity of the latter being set to zero. Equating the two reflection coefficients provides an effective mass density that depends on frequency and on the incidence angle, except at low frequency. The angle dependence is discussed.