The use of different modal quantities for damage identification

The problem of identifying small damages in beam-like structures is studied by defining a suitable inverse problem with different modal quantities including frequencies, mode shapes and modal curvatures. With the aim of making a critical analysis of the different approach followed in the literature, we study a prototype problem of a free-free beam with single and multiple damages. The attention is mainly devoted to modal curvatures. It is shown that by making use of a perturbative solution of the equation of motion of a damaged beam, it is possible to obtain a closed form relationship between the modal curvature differences due to damage and the damage distribution itself. This information is added to the contributions of other modal quantities, frequencies and mode shapes, to improve the inverse problem of damage identification and to eliminate possible redundant solutions. On the other side, the variations of the curvature due to damage is concentrated at damage location and this circumstance can lead to difficulties in its detection. The results of the proposed approach are validated by using the results of an experimental campaign carried out by the authors.