Element stiffness index distribution method for multi-crack detection of a beam-like structure

Abstract

In this article, a method using “element stiffness index distribution” for multi-crack detection of a beam-like structure is presented. The element stiffness index distribution is defined as a vector of norms of sub-matrices corresponding to element stiffness matrices calculated from the reconstructed global stiffness matrix of the beam. When there is a crack at an element, the element stiffness index of that element will be changed. Therefore, by monitoring the change in the element stiffness index distribution, the crack can be detected. A significant peak in the element stiffness index distribution is the indicator of the crack existence. The crack location and the crack depth can be determined from the location of the peak and the height of the peak. In this study, the global stiffness matrix is reconstructed from the measured frequency response functions instead of mode shapes to avoid some limitations of the mode shape-based methods for crack detection. Numerical simulation results for the cases of single crack and double cracks are provided. The results showed that cracks with a depth as small as 10% of the beam height can be detected by the method. The proposed method can be applied with the noise level up to 10%.