Damage detection approach based on the second derivative of flexibility estimated from incomplete mode shape data

The presence of damage in a structural member causes local and global deterioration of structural performance. The stiffness and flexibility can be predicted using the measured mode shapes. The stiffness and flexibility are estimated because it is not easy to collect the complete modal data corresponding to full modes and degrees of freedom (DOFs). The prediction using the lowest few modes provides a more accurate flexibility prediction compared with the stiffness. This work indicates that the updated flexibility matrix can extract more information concerning the state of the structural health compared with the stiffness matrix. Additionally, incomplete measurement data should be expanded to construct the flexibility matrix at damaged state. This study derives the analytical methods used to update the flexibility matrix based on an expanded full set of DOFs and to detect damage using the updated flexibility curvature. The validity of the proposed method is evaluated using a numerical experiment, and the method's effectiveness depending on the number of truncated modes is investigated.