Most of diagnostic techniques used within the class of beam‐like structures are based on the requirement that the damage location closely matches with the calculated and the observed frequency changes. Since these variations are usually mild, one expects that frequency sensitivity to damage plays an important part in the crack identification. Here we show that frequency sensitivity for any beam‐like structure can be explicitly evaluated on the basis of the undamaged system by using a general perturbation approach. The usual jump conditions are taken along with the Freund‐Herrmann concept of using a “spring” to represent the effect of the crack in a section. Then, frequency sensitivity turns to be proportional to the potential energy stored, for the relevant mode shape, at the cross section where the crack occurs. Moreover, the ratios of the frequency changes of various orders are independent of the severeness of the crack and this seems to explain their usefulness in the localization of the damage in prac...

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 ofthe beam. The analysis is based on an explicit expression of the frequency sensi tivity 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 posi tions 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 iden tification are affected by errors relatively small with respect to the frequency-induced changes, then damage identification leads to satisfactory results.