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.