The closed form of the sensitivity of modal flexibility for a real undamped system is derived based on the algebraic eigen sensitivity method. The formula is then adopted to detect the damage location and severity. The merit of the proposed approach over many other exiting modal flexibility sensitivity-based schemes is that it eliminates the adverse effect of the truncating higher-order modes. Moreover, the proposed approach could identify results with sufficient accuracy by employing one mode or multiple modes. To tackle the operational mode shape normalization problem ascribed to the unknown ambient excitation, the scaling factors are employed. A number of assumed damage scenarios in beams has been used to demonstrate the applicability of the proposed damage detection method. It is demonstrated that the proposed method is not sensitive to noise, and it can effectively identify single and multiple damage.
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