Zhu W., Xu G., Emory B.

A robust iterative algorithm is developed to accurately identify the locations and extent of small to large levels of damage in beam structures using 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 numerical and experimental means on cantilever aluminum beams with different damage scenarios. While the resulting system equations are severely underdetermined and there are infinitely many solutions in each iteration, in most cases the minimum norm solution from the generalized inverse method leads to the correct solution at the end of the iterations. When there exist nonunique solutions for certain damage locations, a new method is developed to enrich the measurement information by modifying the structure in a controlled manner and measuring the 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 for such a damage location. Numerical and experimental results are compared in detail and excellent agreement is found. Results show that, with the iterative algorithm, damage in beam structures can be accurately detected using the first several measured natural frequencies. This is a significant finding as it is much easier to measure the natural frequencies of a structure than the mode shapes.