Analytical model for the prediction of the eigen modes of a beam with open cracks and external strengthening

The aim of this study is to develop an analytical model of a beam with open cracks and external strengthening which is able to predict its modal scheme components (natural frequencies and mode shapes). The model is valid as far as the excitation level is low enough not to activate non linear effects. The application field of the model are either the prediction of the efficiency of the reinforcement or the non destructive assessment of the structural properties. The degrees of freedom associated to the fault lips must be taken into account in order to introduce the effect of the external strengthening. In a first step, an analytical formulation of a beam with thin notches is proposed according to the references. The model is then extended to incorporate the strengthening consisting in a longitudinal stiffness applied in the vicinity of the cracks. In a second step, the analytical results are compared with these obtained from a finite element simulation.