Anisotropic dynamic mass density for fluid–solid composites

By taking the low frequency limit of multiple-scattering theory, we obtain the dynamic effective mass density of fluid–solid composites with a two-dimensional rectangular lattice structure. The anisotropic mass density can be described by an angle-dependent dipole solution, to the leading-order of solid concentration. The angular dependence vanishes for the square lattice, but at high solid concentrations there is a structure-dependent factor that contributes to the leading-order solution. In all cases, Wood's formula is found to be accurately valid for the effective bulk modulus, independent of the structures. Numerical evaluations from the solutions are shown to be in excellent agreement with finite-element simulations.