Frequency reduction in elastic beams due to a stable crack: numerical results compared with measured test data

The presence of a crack could not only cause a local variation in the stiffness, but it could affect the mechanical behaviour of the entire structure to a considerable extent. The frequencies of natural vibrations, amplitudes of forced vibrations and areas of dynamic stability change due to the existence of such cracks. The vibration characteristics of cracked structures can be useful for non-destructive testing. In particular, the natural frequencies and mode shapes of cracked beams can provide insight into the extent of damage. The beam has been schematized as a 2-D continuous medium and discretized by means of quadrilateral finite elements. The lowest three natural frequencies (and the associated mode shapes) of the cracked cantilever beam, were obtained via both the modal and spectral analyses, and were compared with experimental data from literature in order to assess the reliability of different models of crack state, namely open crack and contact crack. Both the experimental and numerical results reveal the significant influence of the opening and closing conditions of the crack on the frequency reduction; namely this reduction decreases as more realistic contact phenomena are considered at crack interfaces.