2. Prediction of Forced Response Using Expansion of Perturbed Reduced Order Models with Inexact Representation of System Modes

Variability in measured data is a common problem in the engineering practice. Changes in the mass and stiffness of the same structural component can occur due to minor variability in the tolerances used during the production/manufacturing process. Differences can exist between the real physical structure and its mathematical model representation (FEM) as well as the predicted response and the actual dynamic behavior of the system. For models in which limited data exists or is collected, the quality of the equivalent reduced order model is dependent on the retained modal parameters as well as the level of correlation of the mode shapes. Prediction of system level forced response from the expansion of these reduced order models can be affected by the use of inexact representations of the system modes such as those from Guyan reduced models. Furthermore, the reduction methodology used, the degrees of freedom selected, as well as the number of retained modes can play an important role in the accuracy of the predicted dynamics of the system.

In this work, a truth model (real answer) is created from the perfect analytical representation of a cantilevered beam. A perturbed variation of the analytical representation of the cantilever beam model is also created to correspond to the simulated imperfections of a FEM of the system. The analytical models will be created to investigate the prediction of the full field dynamic response obtained from the expansion of reduced model information (or data at limited number of DOF) and using the inexact mode shapes of the perturbed model (FEM). The perturbed system representation will have the same geometry and properties as the original unmodified beam (perfect analytical model) but imperfections will be introduced by the addition of mass. The models will be created first at full space as a reference and then reduction techniques will be used to determine the necessary information in order to accurately predict the response at all DOF. Aspects involved in model reduction/expansion, DOF selection, and number of retained modes for the analytical cantilever models are investigated for common reduction techniques such as Guyan condensation and SEREP. The use of a perturbed model (not perfectly correlated to the model) for the expansion of measured real time response data will be shown to produce very accurate full field response even though the model does not perfectly correlate to the real truth model.