A comprehensive crack identification algorithm for beams under different end conditions

Abstract This paper presents a direct mathematical model for the prediction and identification of transverse cracks in beams with different end conditions. The input data for this algorithm are the natural frequencies of the first two bending modes of vibrations of the damaged beam. Using these two input values, and with the availability of accurate frequency measurements and ideal end conditions, the crack location and depth are identified in terms of known beam parameters. Four different end conditions are considered: pinned-pinned, clamped-free, clamped-pinned and clamped-clamped. This mathematical model is based on the assumption that the beam is an Euler-Bernoulli beam and considers open, straight, and transverse cracks in beams with rectangular cross-sections. Although this method assumes high accuracy in measurements and ideal end conditions, requirements that are not always guaranteed in practice, the results obtained help as an initial estimate of the severity and proper location of a crack.