Updating Substructure Models With Dynamic Boundary Conditions

In recent years procedures for updating analytical model parameters have been developed by minimizing differences between analytical and preferably experimental modal analysis results. Provided that the initial analysis model contains parameters capable of describing possible damage these techniques could also be used for damage detection. In this case the parameters are updated using test data before and after the damage. Looking at complex structures with hundreds of parameters one generally has to measure the modal data at many locations and try to reduce the number of unknown parameters by some kind of localization technique because the measurement information is generally not sufficient to identify all the parameters equally distributed all over the structure. Another way of reducing the number of parameters shall be presented here. This method is based on the idea of measuring only a part of the structure and replacing the residual structure by dynamic boundary conditions which describe the dynamic stiffness at the interfaces between the measured main structure and the remaining unmeasured residual structure. This approach has some advantage since testing could be concentrated on critical areas where structural modifications are expected either due to damage or due to intended design changes. The dynamic boundary conditions are expressed in Craig-Bampton (CB) format by transforming the mass and stiffness matrices of the unmeasured residual structure to the interface degrees of freedom (DOF) and to the modal DOFs of the residual structure fixed at the interface. The dynamic boundary stiffness concentrates all physical parameters of the residual structure in only a few parameters which are open for updating. In this approach damage or modelling errors within the unmeasured residual structure are taken into account only in a global sense whereas the measured main structure is parametrized locally as usual by factoring mass and stiffness submatrices defining the type and the location of the physical parameters to be identified. The procedure was applied to identify the design parameters of a beam type frame structure with bolted joints using experimental modal data.