Estimating the mass density distribution from ultrasonic dispersion curves

Among non-destructive testing techniques, ultrasonic guided waves have been shown to be a very effective diagnostic tool. This diagnostic strategy aims to use Lamb mode information contained in dispersion curves to infer the elastic and structural characteristics of structures such as plates and rods. In the present work, a first numerical study is performed in order to estimate the distribution of the density through the thickness of semi-infinite plates on the basis of the available dispersion data. The resulting inverse problem is solved by assuming the knowledge of some points belonging to the first Lamb modes and imposing the minimization of the distance between actual and predicted frequencies. The reconstruction of such detailed information certainly constitutes an important challenge, but it can be usefully exploited in several applications such as the early detection of corrosion in steel structures and in the spatial distribution of tissue-level properties inside cortical bones – information useful for the diagnosis of osteoporosis disease. The proposed computational approach is based on a semi-analytical finite element formulation of the reference model and a multigrid-like optimization of the distance between the actual and the predicted eigenfrequencies. Its validation was pursued by an extensive numerical experimentation aiming to point out the influence of the kind and the amount of the used known data, to assess the reliability of the inversion algorithm and the effects due to the presence of noise in the measured data.