FRF-based finite element model updating for non-viscous and non-proportionally damped systems

All structures exhibit some form of damping, but the characterization of damping is not well-understood, and there is no universal damping model for the dynamic systems. Recently, model updating methods have been used to update or identify the damping matrix in dynamic systems. Most of the finite element updating methods assume viscous and proportional damping models for updating or identifying of damping matrix. In this paper, a new finite element model updating method is proposed in which the damping model is assumed as non-viscous and non-proportional. A parametric exponential non-viscous damping model has been used to model the damping in the dynamic system. The proposed method is the frequency response function (FRF)-based updating model, which updates the non-viscous and non-proportional damping matrix in the dynamic system. The effectiveness of the proposed damped finite element updating method is demonstrated by a numerical example and actual laboratory experiments. First, a numerical study is performed on a cantilever beam structure with non-viscous and non-proportional damping. The numerical study is followed by cases involving actual measured data. Joints and boundary conditions are assumed as a major source of damping, therefore joints and boundary conditions are modelled using relaxation functions and damping coefficients. The updated results have shown that the proposed damped element model updating method can be used to derive accurate models for the non-viscous and non-proportional damped systems. This is illustrated by matching complex FRFs obtained from the updated model with from the experimental data.