Using complex modes for 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 the test/analysis differences of natural frequencies and real modes. However, in the case of non-proportionally damped structures the experimental modal analysis yields complex eigenvalues and modes. One way to use these complex modal data for model updating is to extract the underlying real modes from the complex modes by approximate mathematical procedures, which, however, are 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 a previous paper [11] a method was presented allowing to include an analytical non-proportional damping matrix in the computational updating procedure. The method utilizes the factors of local substructure damping matrices as additional updating parameters (so-called Rayleigh factors) which results in a physical non-proportional damping matrix. 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. In contrast to the classical procedure the Rayleigh factors are not used in the objective function to be minimized but are fitted directly to the experimental modal damping ratios within each iteration step. The uncertain updating parameters are only related related to stiffness and mass properties. They are identified as usual by minimizing an objective function containing the test/analysis differences of the complex eigenvalues and modes. In the present paper the theory behind this approach is summarized and additional experiences with the method arc reported from an application to a laboratory test structure with a local damping device designed to generate non-proportional damping behaviour. The prediction quality of the updated model was checked by comparing not only the analytical and experimental modal data used in the objective function for computational parameter updating but also by comparing the analytical and experimental frequency response functions which were not used during the numerical updating process.