Detection of spherical inclusions in a bounded, elastic cylindrical domain

In this work we study the theoretical background behind non-destructive testing (NDT) evaluation as it pertains to the identification of a spherical inclusion inside a circular cylinder. The cylinder is a linear, homogeneous and isotropic medium, bounded in 3D space, while the inclusion contains an ideal fluid. The excitation consists of a normal, time-harmonic and uniform pressure applied on one of the transverse cavity faces, while the remaining surfaces remain traction-free. Next, the displacement fields generated inside and outside the inclusion are expressed in terms of Navier eigenvector expansions. An analytical solution is subsequently recovered for this boundary value problem, which allows for a reconstruction of the harmonic displacement field generated on the outer surfaces of the cylinder. Next, this solution is numerically processed and a number of cases are solved, whereby the inclusion is placed at various stations inside the cylinder. The numerical results clearly demonstrate that in an inverse problem situation, the present measurements clearly show where the inclusion is centered and also give a good estimate of its size.