Hybrid sensitivity matrix for damage identification in axially functionally graded beams

Abstract

A sensitivity-based finite element model updating approach is presented to identify the local damages in axially functionally graded (AFG) beams. The local damage is simulated by a reduction in the elemental Young's modulus of the beam. In the forward analysis, free vibration analysis is conducted to obtain the natural frequency of the beam. Then forced vibration responses of the beam under external force are obtained from Newmark direct integration. In the inverse analysis, an objective function is established and a sensitivity-based finite element model updating approach is used to identify the local damages in the beam. Two numerical examples are investigated to illustrate the correctness and efficiency of the proposed method. Damage identification results from measured natural frequencies and the dynamic responses from different excitation forces are compared. The effects of measurement noise on the identification results are investigated. Studies in this paper indicate that the proposed method is efficient and robust for identifying damages in the axially functionally graded beams. Good identified results can be obtained from the short time histories of a few number of measurement points and the first several natural frequencies.