Crack Identification in Multi-Span Beams on Elastic Foundation by Using Transfer Matrix Method

In this study, an analytical based approach is proposed for detection of cracks in multi-span Euler-Bernoulli beams on Winkler foundation. Transfer matrix method (TMM) is used for both forward and inverse problems. The crack is modeled by means of a linear rotational spring. For the forward problem, natural frequencies of intact and cracked multi-span beam models are calculated via TMM for two different support arrangements and the results are compared with those obtained using finite element method (FEM). In the inverse problem, the crack location and crack length are calculated based on the natural frequencies obtained from FEM simulations using plots of rotational spring flexibilities versus crack location. The predicted crack properties are tabulated with actual data. It is seen that considering elastic foundation slightly decreases the accuracy of crack depth prediction for multi-span beams. However, the accuracy of localization of crack is not affected by Winkler foundation.