Abstract:Scattering by a spherical obstacle of a plane longitudinal wave propagating in an isotropically elastic solid is computed. Expressions for the scattered wave and the total scattered energy are given. Three special types of obstacle—an isotropically elastic sphere, a spherical cavity, and a rigid sphere—are discussed in detail, especially for Rayleigh scattering. The result for the isotropically elastic sphere is compared with the well-known result of scattering of a plane wave propagating in an ideal fluid by … Show more
“…Separation of variables in certain coordinate systems gives a solution in the form of an eigenfunction (special function) expansion for problems with simple penny-shaped cracks [1], cylindrical [2,3] or spherical [4,5] inclusions in an infinite full or an infinite half space. Semi-numerical techniques also predict elastic wave propagation for isotropic [6,7] or transversely isotropic [8,9] materials.…”
Section: Forward Problem and Model Reviewmentioning
“…Separation of variables in certain coordinate systems gives a solution in the form of an eigenfunction (special function) expansion for problems with simple penny-shaped cracks [1], cylindrical [2,3] or spherical [4,5] inclusions in an infinite full or an infinite half space. Semi-numerical techniques also predict elastic wave propagation for isotropic [6,7] or transversely isotropic [8,9] materials.…”
Section: Forward Problem and Model Reviewmentioning
“…A is a constant for a given material, Po is the density of material with no voids, g is dependent on the shear and longitudinal wave speed ratios [11), and E is the Young's modulus. For the calculations presented here, literature values were used for the T300 / 5208 uniaxial composite.…”
The determination of levels of porosity is important in the engineering uses of graphite fiber/polymer matrix composites, since the interlaminar shear strength can be greatly reduced by excessive porosity [1). Research in making nondestructive evaluations using ultrasonics as the probing energy has taken many directions. Hsu [2) has successfully modeled the frequency dependent attenuation to predict porosity levels in composites. Kline [3) has extended the work of Hashsin and Rosen [4) to determine the porosity and fiber volume fraction of composites by solving for the elastic coefficients of the composite structure. The propagation of leaky Lamb waves [5) has also been used to model porosity levels.
“…More complex work has concentrated on a detailed analysis of the scattering occurring in porous, polycrystalline and two phase materials. For discrete scatterers in a homogenous matrix, the theory of Ying and Truell [18] describes the attenuation of longitudinal waves. An examples of the application of this theory is to the experimental data of Kinra et al [19] for a system of lead inclusions in an epoxy matrix.…”
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