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.
The new cross spectral energy method(CSEM)is proposed for maintaining cable-stayed bridge safe-ty by the measurable output-only vibration response.Damage assessment of real structures is limited by aseries of problems such as unknown ambient excitation forces,errors introduced by system identification,incomplete dynamic measurements,etc.Thus the methodology based on cross spectral energy of eachsubstructure member is derived to meet these challenges.The novel damage index does not require anymodal or parameter identification technology.It can be calculated directly from vibration test data.In or-der to evaluate the efficiency of the presented methodology,a three dimensional(3D)actual cable-stayedbridge model with one or more damaged positions under operational conditions was studied.In order totestify the reliability of damage detection method,the response data was polluted by the random noise.Itis proved that the proposed method can successfully localize all damage cases even in noisy data.Withthe help of examples,the CSEM can potentially be applied as a nondestructive evaluation technique(NDT)for on-line health monitoring of cable-stayed bridges with minimum disruption of its operations.
