The dynamic non-linear behaviour of beams with closing cracks Salvatore Caddemi 1 , Ivo Caliò 1 , Massimo Marletta 1 1 Department of Civil and Environmental Engineering, University of Catania, Italy E-mail: scaddemi@dica.unict.it, icalio@dica.unict.it, marletta@dica.unict.it Keywords: Concentrated cracks; Euler-Bernoulli beam; Non-linear dynamic response; Damaged beams; Closing cracks. SUMMARY. In this study the nonlinear dynamic response of beam in presence of multiple concentrated closing cracks is addressed. The overall behaviour of such a beam is nonlinear due to the opening and closing of the cracks during the dynamic response, however it can be regarded as a sequence of linear phases each of them characterised by different number and positions of the cracks in open state. The response of the beam is evaluated by determining the exact modal properties of the beam, in each linear phase, and evaluating the corresponding time history linear response through modal superposition analysis. Appropriate initial conditions at the instant of transition between two successive linear phases have been considered and an energy control criterion has been enforced with the aim of establishing the sufficient number of modes that must be taken into account in order to obtain suitable results. Some numerical applications are presented in order to investigate the dynamic non-linear behaviour of beams with closing cracks. 1 INTRODUCTION In the last decades several authors devoted considerable interest in procedures aiming at the identification of the state of damage of a structure by processing its dynamic response. This increased interest has led to improvements of the existing methods as well as to developments of new procedures for the analysis of the dynamic response of damaged structures in terms of both forward and inverse problems. Most of the procedures proposed in the literature are based on the strong assumption that the damaged structure behaves linearly during the dynamic response, however various theoretical and experimental studies have demonstrated that in some cases a state of damage in a structure can cause a nonlinear behaviour in its dynamic response. A relevant problem within the context of the nonlinear response of damaged structure is that concerned with the so called ‘closing crack’, i.e. a crack which opens and closes during the dynamic response causing nonlinear structural behaviour. This phenomenon was observed experimentally by Gudmunson [1] while performing dynamic tests in a cantilever beam aimed at correlating the position and the extension of the crack with the measure of the variation in natural frequencies. There are different approaches for crack modelling in beam structures reported in the literature; a large part of the considered approaches can be attributed to one of the following categories: spring models or elastic hinges, local stiffness reduction, and finite element models. Friswell and Penny in [2] compare some different approaches for crack modelling and demonstrate that, for structural health monitoring using low frequency vibration, simple models of crack flexibility based on beam elements are adequate. The latter paper also addresses the effect of the excitation for the case of closing cracks, where the beam stiffness can be considered bilinear, depending on