Antiplane coherent scattering from a slab containing a random distribution of cavities

Abstract

The scattering of antiplane waves from a slab region containing a random distribution of cylindrical cavities is investigated. The cavities have a uniform probability density in the slab region and the solid is homogeneous and isotropic on either side of the slab. A general equation for the coherent motion in the solid is derived in terms of the average exciting displacement near a xed cavity. As in Foldy's approach, it is assumed here that the average exciting displacement near a xed cavity is equal to the average total displacement. With this assumption, the equation for the coherent motion reduces to an integrodi¬erential equation, which is solved in closed form by using a Fourier transform technique. The closed-form solution greatly reduces the computational costs, and allows more direct investigation of the multiple scattering than is done elsewhere. Results for the amplitudes and phases of the re®ected and transmitted waves outside the slab are plotted versus the frequency for several values of the cavity density and slab thickness. These results are expected to be valid for low cavity density.

Elastic wave propagation through a random array of dislocations

“…The case of discontinuous heterogeneities has been mainly studied to account for inclusions in the medium. 24,[30][31][32][33][34][35] In this case, boundary conditions of force and displacement continuity at the inclusion surface have to be considered. In both cases, the problem of scattering by the random distribution of weak elastic heterogeneities can be solved starting from an integral representation for the scattered field and considering simplifications to reach a desired order of accuracy, as the Born approximation 28,32 or the averaged T-matrix approximation.…”

Effective wavenumbers and reflection coefficients for an elastic medium containing random configurations of cylindrical scatterers

“…In the case of immersed fluid cylinders with a sound-speed that is close to that of the surrounding fluid, Martin and Maurel [22] show that Linton and Martin's formula [18] can be derived from Lippman-Schwinger's equation without use of the QCA, thus providing a link between distinct formalisms based on Green functions and multipole expansions. Shear-horizontal elastic waves (SH) are also scalar-type waves, and the effective dynamic properties SH waves in composites made of elastic cylindrical fibers randomly distributed in another elastic solid have been calculated by Aguiar & Angel [2] and Aristégui & Angel [4]. They show that the effective mass density and the effective shear stiffness are complex valued and frequency dependent.…”

Interface Effects and Coherent Waves in Porous Elastic Media

“…The integro-differential equation (2.13) can be rearranged by changing the order of integrations. The result, which is given by Equation (3.42) in [9], has the form In (5.5), 1y2 is defined for all y in 1 and is the periodic extension with period 2 1 h 2 12 of u 4 1y2, where y is now in the interval 16 h 6 15 h 2 12. This method yields a linear system of equations for the coefficients m .…”

“…Then, the dimensionless average total displacement u satisfies the integro-differential equation (see [9])…”

“…Scattering by multiple scatterers has been considered in a number of works, as for example in [9,10,11,12,13]. In the special case where scatterers are bubbles, as in biological tissue, some representative works can be found in [14,15,16].…”