Many methods for the assessment of structural damage based on vibration-based technique are surveyed for many decades. In this paper, an effective damage detection methods based on numerical and experimental evaluation of structural damage is presented by sensitivity of modal strain energy and using a new model updating optimization function. First, damage localization in the dynamic structures is formulated by fundamental modal strain energy (MSE) to precisely locate the eventual damage of a structure. With location determined, the corresponding damage extent can be obtained by sensitivity of modal strain energy based on changes in the stiffness components. Subsequently, using of sensitivity matrix and difference between mode shapes of healthy and damaged structures, a new optimization function is defined to accurately estimate the damage severity. For verification of the proposed methods, two illustrative examples as a numerical model of a cantilever beam and a 3-story laboratory frame as experimental model are used. In the experimental investigation, modal analysis with impact hammer is carried out to laboratory frame and vibrational modes are identified as real data. Eventually, results show that the modal strain energy indicator can be exactly detected the location of damage. Then, the estimated damage extent indicates the proposed method based on sensitivity of modal strain energy and minimization of optimization function can provide the convenient results in the numerical and experimental evaluations.

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