### Numerical and experimental studies for crack detection of a beam-like structure using element stiffness index distribution method

#### Abstract

In this paper, numerical and experimental studies for crack detection of structures using "element stiffness index distribution" are 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. By inspecting 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 is determined by the location of the peak and the crack depth can be determined from the height of the peak. The global stiffness matrix is calculated from the measured frequency response functions instead of mode shapes to avoid limitations of the mode shape-based methods for crack detection. Numerical simulation results for the cases of beam-like structures are provided. The experiment is carried out to justify the efficiency of the proposed method.

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