Identification of multiple cracks in a beam using vibration amplitudes

A simple method to identify multiple cracks in a beam using the vibration amplitudes is presented. The cracks are modeled as massless rotational springs and the forward problem is solved using the finite element method. The inverse problem is solved iteratively for the crack locations and sizes using the Newton–Raphson method and the singular value decomposition method. A two-dimensional finite element model is built to simulate the experimental results and to provide vibration amplitude measurements. The difficulty of identifying multiple cracks without a priori knowledge of the number of cracks is overcome by comparing the residual sum of squares of each solution with assumed number of cracks. The crack locations are estimated accurately and the accuracy of the crack size estimations are to be enhanced greatly by an improved torsional stiffness model.