The detection of cracks in beams using chaotic excitations

In the field of structural health monitoring (SHM), vibration-based SHM is one of the general approaches to detect and quantify damage to a structural system. Recently, progress has been made by using chaotic excitation signals and attractor-based analysis to detect damage in a structure. In this paper, a new approach for crack detection is explored by means of numerical simulations, using a chaotic signal as an input excitation and attractor-based measures. A cracked beam is modelled as a single degree of freedom piece-wise linear system whose stiffness is different during compression and expansion of the crack. To utilise this feature of the cracked beam, the single-phase portrait of the structural output is divided into two parts corresponding to the compression and expansion of the crack. Then the dissimiliarity between these two halves of the attractor are examined as a function of crack size. The measures introduced in this work are the half-space correlation dimension, which is the correlation dimension measured on one-half of the attractor, and the Hausdorff distance between the two attractors halves. For these two attractor-based measures, their variations are investigated with respect to crack size to find whether they are appropriate crack indicators or not.