Vibration-based damage detection techniques use the change in modal data as an indicator to assess damages in the structure. Knowing the structural dynamic characteristics of the healthy and damaged structure, the estimation of the damage location and severity is possible by solving an inverse problem. This paper presents a mathematical expression relating damage location and depth to the frequency shifts of the bending vibration modes. This expression permits the extraction of a series of coefficients that characterize each damage location and are independent of the damage severity. The vector aggregating these coefficients for a given location constitutes a Damage Location Indicator (DLI) that unambiguously characterizes the position of a geometrical discontinuity in the beam. A set of vectors typifying all locations along the beam may be used as patters opposable to the damage signature found by measurements. The similarity between the signature and one of the patterns indicates the location of damage
