A multiple scattering theory for elastic wave propagation in discrete random media

Abstract

A multiple scattering theory for elastic wave propagation in a discrete random medium is presented. A self-consistent multiple scattering formalism using the T matrix of a single scatterer in conjunction with the quasicrystalline approximation (QCA) and a self-consistent pair correlation function is employed to study the phase velocity and coherent attenuation of elastic waves by a random distribution of cavities and elastic inclusions embedded in an elastic matrix. Both uniform and Gaussian size distributions are assumed. The theoretical results obtained in this study are shown to be in excellent agreement with experimental observations.

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

“…26 In these studies, the scattered fields from each scatterer are summed, and then ensemble-averaged over all possible (usually) random configurations of scatterer positions. A solution to the equations can only be obtained by making an assumption about the incident field at each scatterer-the so-called closure assumption.…”

Ultrasonic Attenuation Measurement by Backscattering Analysis

“…These distributions are uncorrelated, therefore dP = ~~~2 Y(k). (6) Of course the finite diameter transducer will be somewhat sensitive to directions other than its axis as well, but we can use the total scattering cross-section anyway as a very good approximation because the transducer diameter is much higher than the average pore diameter. Consequently, regardless of the frequency, the scattered energy will be radiated into a much higher solid angle than the angle of acceptance of the transducer.…”

“…Recently several studies which discuss the porosity induced ultrasonic attenuation have appeared [1][2][3][4][5][6][7][8]. Porosity assessment by ultrasonic attenuation measurement involves two principal problems: first, how to relate the porosity induced ultrasonic attenuation to porosity parameters such as average pore radius and volume fraction, and second, how to separate the sought porosity induced attenuation from other components contributing to the actually measured total attenuation.…”

A comparative study on propagation of elastic waves in random particulate composites

“…Thus, it is rather impossible to guarantee accuracy of their results at low frequencies. Varadan et al (1982Varadan et al ( , 1985 developed T-Matrix method in multiple scattering of the waves using quasi-crystalline estimations and introducing a pair-correlation function. A similar work was launched by Mal & Bose (1974) who analytically studied the scattering of the plane wave by spherical elastic inclusions which were randomly distributed within an infinite matrix.…”