Identification of crack characteristics in beams by using modal frequencies and inverse problem

Abstract

Detection of cracks in mechanical components as early as possible enables monitoring structural health and scheduling efficiently the maintenance tasks such as replacing the critical parts just in time. Vibration analysis based techniques for crack detection have been largely considered in the framework of beam-like structures. This methodology relies essentially on the observed changes of beam frequencies and mode shapes induced by the presence of damage. In the present work, using an explicit analytical model assessing the effect of a crack on beam strain energy, the beam first resonance frequencies as they depend on a single crack defect characteristics were evaluated. The crack equations were obtained by means of fracture mechanics approach. Variations of the first beam frequencies and modes shapes were then related explicitly to the location and depth of the crack. Measuring the beam frequency changes and monitoring their variations can be used to perform identification of the crack defect parameters by solution of an inverse problem.