Optimal Finite Difference Schemes for Multiple Damage Identification in Beams

This paper presents an experimental and numerical study on multiple damage localization in a beam. The modal rotations of an aluminum beam were measured with shearography and post-processed to obtain the modal curvatures. The modal curvatures, which are computed by finite differences, are used as damage indicators. In most approaches available in the literature, the modal curvatures are defined from the modal displacements, requiring the computation of the second order derivate. In the present approach, since the modal rotations are available, the curvatures are obtained by computing only the first order derivative, reducing the propagation of measurement errors. Optimal samplings for both the forward and the central finite difference schemes, the latter with three and five points formulas, are derived. The results of applying these three finite difference formulas are compared, showing that both central finite differences allow for a better representation of the experimental modal curvature. Therefore, the perturbations on the modal curvatures are better identified, thus clearly indicating the damage presence.