Structure Damage Detection Based on Modal Flexibility Matrix

The damage detection method based on model updating is more convenient and advanced than the traditional instrument detection techniques. In this method, it is not necessary to known the damage locations of structures. The model updating methods are usually based on the targets of mode frequencies and shapes updating. However, the structure damage has little effect on the mode frequencies and shapes. So, the damage can hardly be detected with traditional updating methods which take the mode frequencies and shapes as objectives. In this paper, the mode flexibility matrix, which is very sensitive to the structure damages, was introduced. The structure damage detection method with the flexibility matrix as the objective was studied. A rectangular iron panel with holes was selected as the object of study. It was divided into 31 pieces in longitudinal direction. The mode flexibility matrix sensitivity to each equivalent modulus was calculated. The objective function was established with sensitivity matrix and mode flexibility residual. Then, the ill posed equations of objective functions were solved by regularization method. The objective function converged with nine iterations and the result of damage identification was in very good agreement with the real value. It is verified that the method is accurate and practical.