Issue 29

P. Casini et alii, Frattura ed Integrità Strutturale, 29 (2014) 313-324; DOI: 10.3221/IGF-ESIS.29.27 313 Focussed on: Computational Mechanics and Mechanics of Materials in Italy Crack detection in beam-like structures by nonlinear harmonic identification Paolo Casini, Fabrizio Vestroni University of Rome la Sapienza p.casini@uniroma1.it , vestroni@uniroma1.it Oliviero Giannini University Niccolò Cusano oliviero.giannini@unicusano.it A BSTRACT . The dynamic behavior of beam-like structures with fatigue cracks forced by harmonic excitation is characterized by the appearance of sub and super-harmonics in the response even in presence of cracks with small depth. Since the amplitude of these harmonics depends on the position and the depth of the crack, an identification technique based on such a dependency can be pursued: the main advantage of this method relies on the use of different modes of the structure, each sensitive to the damage position in its peculiar way. In this study the identification method is detailed through numerical examples tested on structures of increasing complexity to evaluate the applicability of the method to engineering applications. The amount of data to obtain a unique solution and the optimal choice of the observed quantities are discussed. Finally, a robustness analysis is carried out for each test case to assess the influence of measuring noise on the damage identification. K EYWORDS . Fatigue crack; Damage identification; Nonlinear dynamics; Cracked beam model. I NTRODUCTION he occurrence of cracks in civil or mechanical systems leads to dangerous effects for the structural integrity and causes anomalous behaviors. To not compromise the safety, the detection of a crack in the early stage is of great interest. The presence of a crack not only causes a local variation in the mechanical characteristics of the structure at its location, but it also has a global effect involving the entire structure. For this reason, the dynamic characterization of cracked structures can be used for damage detection in non-destructive tests and, among the various techniques, vibration-based methods provide an effective means of detecting fatigue cracks in structures [1-7]. The vibration-based detection methods exploit the fact that damage in a structure alters its dynamic properties: in particular the presence of cracks can be disclosed by modifications in the linear response (i.e., modal frequencies, damping and shapes associated with each natural frequency, curvature of mode shapes etc.) as well as by the occurrence of nonlinear effects (sub- and super-harmonics, bifurcations, internal resonances etc.). There are two main categories of crack models used in vibration-based detection methods: open crack and breathing crack models. In the first case it is assumed that the crack in a structural member remains open during vibration. This assumption is usually satisfied in notched beams and when the damage is rather large; this model avoids the complexity resulting from nonlinear behavior when a breathing crack is presented. On the contrary, breathing behavior is generally T

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