The paper of McAdams et al. (ASME J. Appl. Mech. 74, pp. 191–202) explored two different approaches for damage detection in vibrating beams having both manufacturing variations in geometry and crack damage. One of the approaches, however, has a significant error in its formulation. The effects of this error on the formulation and the analytical results are discussed.
In Ref. 1, the authors pursued two approaches for damage detection in the presence of geometric variations in cross section due to manufacturing tolerances. They exploit the fact that both the damage and the manufacturing tolerances produce spatial dependence in the beam’s mass density and flexural rigidity, which in turn influences the modal vibration properties of the beam, specifically its natural frequencies. The consideration of such spatial variations has recently attracted attention in the structural health monitoring community, and other researchers (2,3) have proposed related approaches for identifying damage based on this concept, albeit without consideration of manufacturing tolerances.
It should be noted that the authors’ second approach to the damage identification problem makes no use of Eq. 2, so there is no reason to believe that the results obtained via this approach have this source of error. The authors, however, are encouraged to revisit their finite difference analysis in light of the points raised by this discussion.