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Damage detection in flexible structures is a research field and an industrial favorite. If damages in structures, air crafts and ships are not detected and repaired, they will possibly collapse. Damage detection in flexible structures using vibration signals and in particular modal test data is the most suitable method. This method is in fact an NOT technique. In this we will present an analytical method for damage detection in
. undamped flexible structures using modal data (natural frequencies and modeshapes). Reviewing past theories, eigenvalue and eigenmode, sensitivity
equations are used to derive a system of equations relating the shifts in natural
frequencies/mode-shapes to elemental physical parameters. Damage detection is then carried out by solving the extracted system of equations. Also, modal expansion and Nelson method are examined and the better method of solving for eigenmode perturbation is chosen. It is recommended that in solving for repeated eigenmode perturbation with generalzed inverse techniques, orthogonality condition between theoretical modeshapes must be satisfied. The presented mathematical relations are applicable for trusses, beams and frames but the principles of the theory is general. Finally an experimental investigation is carried out and the position of a crack in a frame with this theory detected.