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

This paper presents a diagnostic technique for the identification of two cracks 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 the 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-identification of crack location and severity. The inverse problem is ill-posed; namely, even by leaving symmetrical positions aside, cracks with different severity in two sets of different locations can produce identical changes in the first three natural frequencies. Numerical results show that if the natural frequencies used as data in identification are affected by errors relatively small with respect to the frequency-induced changes, then damage identification leads to satisfactory results.