Model Calibration of Nonlinear Mechanical Systems Using Multi-Harmonic Frequency Response Functions
Abstract: In industry, linear finite element models are commonly employed to represent global structural behavior. It is crucial that the computational models are able to accurately represent the structures’ behavior. This cannot always be achieved by the use of linear models.When vibrational test data show significant nonlinear characteristics, an initial linear finite element model may be judged insufficient in representing the structural behavior. Although an initial model can give a good foundation for the understanding of the dynamic behavior of the structure, the parameters that capture the nonlinear effects are most likely not included. Therefore, a set of candidate parameters controlling the nonlinear effect have to be added. The selection of such candidates is a delicate task which solution is preferably supported by engineering insight into the characteristics of the structure.One part of this work is on the selection of parameters, among all possibly uncertain properties, together with the forming of the objective function to be used for calibration. To obtain precise estimates of the parameters, the objective function data have to be informative with respect to the selected parameters. Further the parameters have to be identifiable. To improve these qualities, a multi-harmonic sinusoidal excitation was designed since the corresponding steady-state responses at the sub- and super- harmonics were shown to contain valuable information for the calibration process. Model calibration of nonlinear systems made by minimizing the differences between predicted and measured multi-harmonic frequency response functions.Further, in the calibration, multi-harmonic frequency response functions need to be calculated recurrently in order to reach convergence; therefore a fast simulation scheme was required. The performance of computations of multi-harmonic frequency response functions calculated using time domain as well as frequency domain simulation techniques were studied and compared.Finally, the proposed calibration method was validated by use of experimental testing on a replica of the Ecole de Lyon nonlinear benchmark structure. It was shown in the validation results that the predictions stemming from the calibrated model matched the experimental data well.
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