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.