A method for structural damage identification using residual force vector and mode shape expansion

A method for structural damage identification using residual force vector and mode shape expansion is presented in this paper. To deal with the incompleteness of measured modal data, a mode shape expansion method is first introduced to match with all degrees of freedom of the finite element model under consideration. And then, the residual force vector is employed to locate the damage position and quantify the damage extent. In order to eliminate the influence of extra errors that caused by mode shape expansion and improve the efficiency of the methodology, residual force vector assurance criterion (RFVAC) is developed to analyze the sensitivity between two sets of residual force vectors in the health and damaged structures after mode shape expansion. Finally, the proposed method is numerically illustrated by a simply supported truss beam with three damage cases. Results indicate that the proposed method is effective for the structural damage identification when the measured mode shapes are incomplete.