Computational model updating of structures with non-proportional damping

The inverse sensitivity approach is most often used in computational model updating to adjust selected stiffness and mass parameters of large order finite element models by minimizing an objective function which includes the test/analysis differences of natural frequencies and real normal modes related to the undamped structure. However, in the case of non-proportionally damped structures the experimental modal analysis in general yields complex eigenvalues and modes. In order to apply presently available updating techniques the real modes are usually extracted from the complex modes by approximate mathematical procedures which is prone to unavoidable approximation errors. The straightforward way would be the direct utilization of the complex modal data in the updating process. In this case the analytical model to be updated would have to include a damping matrix which, however, is usually not known in physical finite element coordinates. In this paper a method is presented for identifying an analytical non-proportional damping matrix within the computational updating process. The method utilizes the factors of local substructure damping matrices as additional updating parameters (so-called Rayleigh factors). The definition of the substructures is user's choice and could, for example, be related to a local discrete damper or to a larger substructure with uniform damping. The Rayleigh factors are not used in the objective function but are fitted directly to the experimental modal damping ratios within each iteration step. The uncertain updating parameters related to stiffness and mass properties are identified as usual by minimizing an objective function containing the test/analysis differences of the complex eigenvalues and modes. The theory was verified by using simulated experimental data and also by using laboratory test data from a structure with a local damping device designed to generate non-proportional damping.