By distributing the concentrated singularities such as a Kelvin doublet along the axis of symmetry we describe the displacement field, in an elastic medium, for various modes of rotation and translation for a rigid prolate and oblate spheroid. The limiting cases of a sphere, a slender body and a thin circular disk are also discussed. All the solutions are presented in a closed form.
RESUMt~En distribuant les singularit6es concentr6es, comme par exemple un doublet de Kelvin, le long des axes de symetrie, nous d6crivons le champs de d6placement en milieu 61astique, pour divers modes de rotation et de translation d'un ellipsoide rigide, oblong ou prolong. Les cas limites d'une sph6re, d'.une aiguille et d'un disque circulaire mince sont aussi discut6s. Toutes les solutions sont present6es sous une forme ferm6e,
The three-dimensional problem of scattering of steady elastic waves from an arbitrarily shaped body is formulated in terms of simultaneous singular integral equations. These basic equations defining the displacement potentials at the surface are two-dimensional Fredholm integral equations of the second kind over the surface of the body. In contrast to other formulations, this procedure is not restricted to a particular shape of the scattering object or to the nature of the incoming wave. However, by assuming the scatterer to be a body of revolution, the integral equations are reduced to one-dimensional Fredholm equations along the axis of the scatterer. The formulation is presented for a fixed rigid scatterer.
The integral equations are solved by approximating the potential functions by a set of polynomials and by satisfying the integral equations in the sense of least squares. The solution yields the surface potentials from which the field potentials or the field displacements are obtained by surface integrals. The numerical results are in good agreement with those obtained by the eigenfunction method for an incoming wave which is a plane shear or longitudinal wave.
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