Finite element model updating of non-proportional and exponential non-viscous damping systems using complex eigenvalues and eigenvectors

This paper proposes a finite element model updating method for non-proportional viscous and exponential non-viscous damping systems using complex eigenvalues and eigenvectors. The exponential non-viscous damping provides complex eigenvalues/vectors for elastic modes and real-valued eigenvalues/vectors for non-viscous modes. This study first highlights the challenges in accurately identifying real-valued eigenvalues/vectors for non-viscous modes with a commonly used system identification method. In contrast, complex eigenvalues/vectors for elastic modes are reliably identified and, therefore, utilized in the proposed model updating approach. Consequently, an optimization formulation is proposed to minimize the difference between the simulated and experimental complex eigenvalues/vectors. The method applies large structures that can contain multiple substructures with different damping properties. For brevity, damping properties are assumed to be uniform over each substructure. In addition, mass-proportional viscous damping and stiffness-proportional non-viscous damping are adopted for each substructure, which results in overall damping being non-proportional. To improve computational efficiency, the analytical gradient of the proposed optimization formulation is derived and implemented. For validation, the model updating of a full-scale steel pedestrian bridge is performed. The method is first validated in simulation and further validated by experimental data considering the statistical properties of system identification results. The proposed method successfully identifies stiffness and damping parameters using only a limited number of measured DOFs and modes.