The use of vibration-based damage identification techniques has received considerable attention in recent years. These techniques rely on changes in some structural dynamic characteristics in order to establish a damage indicator. While various damage indicators have been reported in the literature, those relying only on changes in the natural frequencies are appealing in many aspects. Nevertheless, the use of natural frequencies in damage identification has been faced with several difficulties, such as insensitivity and uniqueness concerns. In an attempt to overcome these obstacles, this paper addresses the development of a damage identification scheme based on changes in the natural frequencies of beam structures through a numerical model formulated by the Spectral Element Method (SEM) in conjunction with an optimization algorithm in a model updating approach to predict the location and extent of damage. The use of the SEM significantly reduces the number of design variables, which makes the search algorithm in the inverse problem faster and more efficient. Damage is modeled as a localized reduction in the beam thickness. Three spectral elements are employed to model an elastic beam with a defect and three variables are realized to model the location, size and severity of damage. A stochastic genetic algorithm was developed to facilitate the search for damage based on a set of measured natural frequencies. The use of the proposed formulation is supported experimentally on a set of free-free beams provided with various damage scenarios, and is shown to be a viable tool in damage identification.

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