Solutions of Damaged Beam Structures under Static Loads and their Use for Identification

In this study Euler-Bernoulli beams in presence of a single concentrated damage, subjected to static loads, are considered. The concentrated damage is modelled as a singularity, described by a Dirac’s delta, in the inertia moment of the cross section. The direct analysis problem is solved within the context of the distribution theory leading to explicit expressions of the response in terms of intensity and position damage parameters. Explicit solutions of the direct analysis problem allows to formulate a damage identification procedure on the basis of experimental measurements. Explicit solutions of the inverse damage identification problem are also provided. Finally, sensitivity of the identified damage parameters to instrumental noise is explored by making use of explicit expressions .