Most of diagnostic techniques used within the class of beam-like struc-
tures 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 pro-
portional 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.
