Effective mass density for periodic solid-fluid composties

Abstract

Effective mass density is one of the basic parameters in the study of acoustic wave propagating in fluid-solid composites. Based on the multiple-scattering theory, an analytic solution of the dynamic effective mass density for composites with solid inclusions immersed in fluids periodically in two dimensions is obtained in the low frequency limit. When the concentration of solid is small, the dynamic mass density can be described by an angle-dependent dipole solution and the angle-dependence vanishes if the structure has a four- or six-fold symmetry. When the solid concentration is getting large, the dynamic mass density differs from the dipole solution and also becomes structure-dependent even for square and hexagonal lattices. The Wood's formula is accurately valid, independent of the structures, at any solid concentrations. Numerical evaluations from the analytic solution are shown to be in excellent agreement with finite-element simulations. In the vicinity of the tight-packing limit, the dynamic mass density exhibits a universal behavior independent of the lattice symmetry. Support of this work comes from KAUST Start-up Package, National Natural Science Foundation of China (Grant No. 10804086), the Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 200804861018) and Hong Kong RGC grant HKUST 604207.