Crack‐Induced Changes in Eigenparameters of Beam Structures

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 practical situations.