Damage detection using a modified laplacian operator on mode shape data

Localized damage to a structure affects its dynamic properties, and much work has been undertaken investigating the variation of natural frequencies with damage. However, use of mode shape data has seen much less effort. This paper develops and presents a technique for identifying the location of structural damage in a beam. The procedure operates solely on the mode shape from the damaged structure, and does not require a priori knowledge of the undamaged structure. The procedure is developed using a one-dimensional finite element model of a beam, and demonstrated by experiment. When damage is severe (a localized thickness reduction of more than 10%), applying a finite difference approximation of Laplace's differential operator to the mode shape successfully identifies the location of the damage. However, when damage is less severe, further processing of the Laplacian output is required before the location can be determined. This post-processing enables the location of thickness reductions of less than 0.5% to be identified. The procedure is best suited to the mode shape obtained from the fundamental natural frequency. The mode shapes from higher natural frequencies can be used to verify the location of damage, but they are not as sensitive as the lower modes. (C) 1997 U.S. Government.