Employing incomplete complex modes for model updating and damage detection of damped structures

In the study of finite element model updating or damage detection, most papers are devoted to undamped systems. Thus, their objective has been exclusively restricted to the correction of the mass and stiffness matrices. In contrast, this paper performs the model updating and damage detection for damped structures. A theoretical contribution of this paper is to extend the cross-model cross-mode (CMCM) method to simultaneously update the mass, damping and stiffness matrices of a finite element model when only few spatially incomplete, complex-valued modes are available. Numerical studies are conducted for a 30-DOF (degree-of-freedom) cantilever beam with multiple damaged elements, as the measured modes are synthesized from finite element models. The numerical results reveal that applying the CMCM method, together with an iterative Guyan reduction scheme, can yield good damage detection in general. When the measured modes utilized in the CMCM method are corrupted with irregular errors, assessing damage at the location that possesses larger modal strain energy is less sensitive to the corrupted modes. © 2008 Science in China Press and Springer-Verlag GmbH