Estimating the dynamic effective mass density of random composites

Abstract

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.

Effective shear speed in two-dimensional phononic crystals

“…Indeed, replacing 2 l=1 by d l=1 keeps (22) intact and replaces the factor 2 by d before μ in (23), which leads to c 2 …”

“…[1][2][3] The recent surge of research into the properties of metamaterials and phononic crystals has heightened attention, particularly for periodic systems. In this context, considerable work has been done on the low-frequency, or quasistatic, limit of the antiplane shear-wave speed in 2D periodic structures (referred to as the "effective speed" c in the following; note that this value also yields the limit of the fundamental velocity branch of shear plate waves).…”

A comparison of stochastic and effective medium approaches to the backscattered signal from a porous layer in a solid matrix

“…35 Based on these newer effective wavenumber derivations, or on the older versions, various workers have identified a set of effective properties for the material, for example, density, modulus, and viscosity. [31][32][33] Of greater interest in the present work, is the determination of the reflection characteristics of a layer, or slab, of material containing scatterers, which has been derived by a number of the same workers, based on the scattering theory formulations described above. [27][28][29][30]36 In summary, what has been established is as follows: (a) The effective material properties of a slab or layer are the same as the effective material properties of a half-space.…”

“…While the effective wavenumber due to scattering theory is well-established for dilute systems, its application to more concentrated systems is still the subject of development. However, there has been a recent emergence of interest in the effective properties of inhomogeneous materials derived from scattering theory; in particular a number of workers [27][28][29][30][31][32][33] have attempted to obtain properties other than the elastic moduli, such as effective density, effective viscosity and the effective reflection and transmission coefficients of both a semiinfinite half-space, and a slab.…”

Simulation of incoherent and coherent backscattered wave fields from cavities in a solid matrix

“…[2][3][4][5][6] For this part of the wave field, therefore, the material can be defined by effective properties corresponding to an equivalent homogeneous medium with the same ultrasonic propagation characteristics. Many different schemes exist for the derivation of these effective properties, including models termed effective medium models, self-consistent models, multiple scattering models, ensemble-average models, and homogenization schemes.…”