Detection and localization of inclusions in plates using inversion of point actuated surface displacements

A numerical simulation is carried out demonstrating the use of plate surface vibration measurements for detecting and locating inclusions within the structure. A finite element code is used to calculate normal surface displacement for both steel and mortar plates subjected to a monochromatic point force. The data is generated for the homogeneous plate and the identical plate within which exists a small rectangular inclusion. It is observed that when the elastic modulus of the inclusion is orders of magnitude lower than the base material, resonances of the inclusion produce large local displacements that are readily observed in the raw displacement data. For more modest moduli differences, there are no such directly observable effects. In this case, three inverse algorithms are used to process the displacement data. The first two are local inversion techniques that each yield a spatial map of the elastic modulus normalized by density. These algorithms successfully detect and localize the inclusion based on its modulus difference from that of the base plate. The third technique uses a form of the inhomogeneous equation of motion to obtain the induced force distribution connected with the inclusion. The spatial mapping of this force also successfully detects and localizes the inclusion.