Identification of two cracks in a simply supported beam from minimal frequency measurements

This paper presents a diagnostic technique for the identification of two cr acks of equal severity in a simply supported beam under flexural vibrations . The crack is simulated by a rotational spring connecting the two adjacent segments of the beam. The analysis is based on an explicit expression of t he frequency sensitivity to damage, and the damaged system is considered as a perturbation of the virgin system. By measuring the changes of the first three natural frequencies, it is possible to study the inverse problem-ide ntification of crack location and severity. The inverse problem is ill-pose d; namely, even by leaving symmetrical positions aside, cracks with differe nt severity in two sets of different locations can produce identical change s in the first three natural frequencies. Numerical results show that if th e natural frequencies used as data in identification are affected by errors relatively small with respect to the frequency-induced changes, then damag e identification leads to satisfactory results.