A robust iterative algorithm is used to identify the locations and extent of damage in beams using only the changes in their first several natural frequencies. The algorithm, which combines a first-order, multiple-parameter perturbation method and the generalized inverse method, is tested extensively through experimental and numerical means on cantilever beams with different damage scenarios. If the damage is located at a position within or of the length of the beam from the cantilevered end, while the resulting system equations are severely underdetermined, the minimum norm solution from the generalized inverse method can lead to a solution that closely represents the desired solution at the end of iterations when the stiffness parameters of the undamaged structure are used as the initial stiffness parameters. If the damage is located at a position within of the length of the beam from the cantilevered end, the resulting solution by using the stiffness parameters of the undamaged structure as the initial stiffness parameters deviates significantly from the desired solution. In this case, a new method is developed to enrich the measurement information by modifying the structure in a controlled manner and using the first several measured natural frequencies of the modified structure. A new method using singular value decomposition is also developed to handle the ill-conditioned system equations that occur in the experimental investigation by using the measured natural frequencies of the modified structure.
Issue Section:
Technical Papers
Keywords:
structural damage detection,
natural frequency changes,
perturbation method,
generalized inverse method,
iterative algorithm,
underdetermined system equations,
cantilever beams,
enrichment of measurement information,
ill-conditioned system equations,
structural acoustics,
condition monitoring,
beams (structures),
cantilevers,
elastic constants,
perturbation theory
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