Analytical and experimental studies on detection of longitudinal, L and inverted T cracks in isotropic and bi-material beams based on changes in natural frequencies

•Analytical formulation for natural vibration of slender beams involving L and inverted T crack are presented.•Paper includes experimental verifications of the proposed methods for both forward and inverse problems.•Virtual tests involving FE results too are given.•Both isotropic and bi-material beams are considered.•In the passing, experimental studies on longitudinal cracks are included. An analytical method for determination of dimensions of longitudinal crack in monolithic beams, based on frequency measurements, has been extended to model L and inverted T cracks. Such cracks including longitudinal crack arise in beams made of layered isotropic or composite materials. A new formulation for modelling cracks in bi-material beams is presented. Longitudinal crack segment sizes, for L and inverted T cracks, varying from 2.7% to 13.6% of length of Euler-Bernoulli beams are considered. Both forward and inverse problems have been examined. In the forward problems, the analytical results are compared with finite element (FE) solutions. In the inverse problems, the accuracy of prediction of crack dimensions is verified using FE results as input for virtual testing. The analytical results show good agreement with the actual crack dimensions. Further, experimental studies have been done to verify the accuracy of the analytical method for prediction of dimensions of three types of crack in isotropic and bi-material beams. The results show that the proposed formulation is reliable and can be employed for crack detection in slender beam like structures in practice.