Structural Damage Detection Using Generalized Flexibility Matrix and Changes in Natural Frequencies

Based on the measured vibration information, a method for detecting reduction in stiffness parameters of a structure using generalized flexibility matrix and changes in natural frequencies is presented in this paper. For incomplete measured data of the first mode shape, dynamic expansion of mode shape is introduced. The generalized flexibility matrix is approximately constructed by using the measured first frequency and the extended mode shape only, and it is further used to detect the possible damaged elements. An iterative algorithm using the changes of the first several natural frequencies only is subsequently used to update the damage extent of these possible damaged elements, while the number of damage-extent parameters to be determined in the algorithm is remarkably reduced. Finally, two numerical examples concerning a two-span beam and a two-story frame are used to illustrate the effectiveness of the proposed method.