An algorithm to assess transversal cracks in composite structures based on natural frequency changes due to damage is proposed. The damage assessment is performed in two steps; first the crack location is found, and afterwards an evaluation of its severity is performed. The technique is based on a mathematical relation that provides the exact solution for the frequency changes of bending vibration modes, considering two terms. The first term is related to the strain energy stored in the beam, while the second term considers the increase of flexibility due to damage. Thus, it is possible to separate the problems of localization and severity assessment, which makes the localization process independent of the beams cross-section shape and boundary conditions. In fact, the process consists of comparing vectors representing the measured frequency shifts with patterns constructed using the mode shape curvatures of the undamaged beam. Once the damage is localized, the evaluation of its severity is made taking into account the global rigidity reduction. The damage identification algorithm was validated by experiments performed on numerous sandwich panel specimens.
Global rigidity of (quasi-)injective frameworks on the line
