On the direct and inverse scattering problem from a spherical inclusion imbedded in a cylindrical elastic bounded domain

In this paper we study the theoretical part behind a non-destructive testing (NDT) method for the identification of a spherical inclusion inside a bounded cylindrical elastic medium. The latter is considered to be linear, homogeneous, isotropic and bounded in 3-D space while the inclusion contains an ideal fluid. We apply a normal, harmonic and uniform pressure load on the one tranverse cavity surface and express the dispacement fields inside and outside the inclusion in terms of Navier eigenvector expansions. The rest of the exterior surface is assumed to be traction free. We solve the problem above and investigate the displacement field on the outer surface of the cylinder. Suitable numerical proccessing is performed at the final stage of the theoretical model. In the inverse problem regime, we show that knowledge of the displacement field on the lateral cylinder surface leads to determination of the inclusions position as well as an estimation of its size.