A two-step procedure for damage detection in beam structures with incomplete mode shapes

In this work, we present a two-step procedure for damage identification in beam structures exploiting modal curvature changes. The reconstruction of modal curvatures requires the knowledge of several mode shape components along the analyzed beam. This requirement is practically unachievable when mode shapes are identified via vibration-based monitoring using a limited number of accelerometers. To overcome this limitation, in the first step of the proposed procedure, we perform a mode shape expansion employing a reduced subset of measured modal components. The remaining measured components are used as control parameters to formulate a first hypothesis on damage location and extent. For this purpose, the expansion procedure is performed considering a number of possible damage scenarios, consisting of a location and a severity (loss of stiffness) of the damage. Using the Total modal assurance criterion (TMAC), we select the expanded modes with the highest degree of correspondence with the measured control components. These expanded modes are thus associated with a first guess of the damage location and severity. In the next step, this initial damage identification is verified through the computation of a modal curvature-based damage index. If the curvature-based damage identification confirms the previous identification, the damage location and extent are determined. The procedure can be easily extended to identify multiple simultaneously damaged elements. The approach is numerically validated using a benchmark beam modeled via finite elements, investigating the influence of different parameters such as noise, position of the control components and beam discretization on the identification success rate. Finally, the procedure is tested on two experimental specimens: a steel beam, with three different damage configurations and a concrete beam progressively damaged with multiple damage locations.