Inversion methods for the detection and localization of inclusions in structures utilizing dynamic surface displacements

Abstract

In this paper, we investigate the feasibility of both detecting and localizing inclusions in structures given a knowledge of dynamic surface displacements. Provided with such displacement information, the equations of motion are utilized to estimate local material parameters through inversion, as well as to indicate the locations of inclusions using a novel generalized force mapping technique. Using a finite element code, numerical simulations were carried out for the determination of the normal surface displacements for both steel and mortar rectangular plates subject to monochromatic point actuation. The data is generated for both homogeneous plates and inhomogeneous plates within which a small rectangular inclusion of differing material parameters is present, and three algorithms are applied to the calculated displacement data. The first two are local inversion techniques which provide a spatial map of the elastic modulus normalized by density, while the third technique utilizes the inhomogeneous form of the equations of motion to obtain an induced force distribution caused by the inclusion. It will be demonstrated that the algorithms can both detect and locate inclusions in structures even when the materail parameter difference of the inclusions and the background medium is relatively low.