Identification of Beam Cracks by Solution of an Inverse Problem

Detection of cracks in mechanical components as earlier as possible enables structural health monitoring and scheduling more effectively 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 literature. This methodology relies essentially on the observed changes of beam frequencies and mode shapes that are 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 were evaluated as function of a single crack defect characteristics. 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 is shown to enable identification of the crack defect parameters by solution of an inverse problem.