Damages Identification in the Cantilever-based on the Parameters of the Natural Oscillations

An approach to parametric identification of damages such as cracks in the rod cantilever construction is described. The identification method is based on analysis of shapes of the natural oscillations. The analytic modelling is performed in the Maple software on the base of the Euler-Bernoulli hypothesis. Crack is modelled by an elastic bending element. Transverse oscillations of the rod are considered. We take into account first four eigen modes of the oscillations. Parameters of amplitude, curvature and angle of bends of the waveforms are analysed. It was established that damage location is revealed by ‘kink’ on corresponding curves of the waveforms. The parameters of oscillation shapes are sensitive to the crack parameters in different degree. The novelty of the approach consists in that the identification procedure is divided into two stages: (a) it is determined the crack location, and (b) it is determined the crack size. Based on analytical modelling, an example of determination of dependence of the crack parameters on its size in the cantilever rod is presented. Study of features of the waveforms during identification of the fracture parameters shows that the features found in the form of ‘kinks’ and local extreme a of the angle between the tangent and curvature of waveforms for different modes of bending oscillations, define the crack location in cantilever. They can serve as one of diagnostic signs of crack identification and allow us to determine its location.