Vibration Frequency Optimization of Jointed Structures with Contact Nonlinearities using Hyper-Reduction

We present a new method for the analysis and optimization of jointed structures with local contact nonlinearities. It is based on nonlinear model order reduction using the Energy-Conserving Sampling and Weighting (ECSW) method (Farhat et al., 2014) for the nonlinear parts of the model, and a Galerkin projection of the complete domain onto a basis spanned by eigenmodes. The analysis of a typical example problem case shows that accurate results and substantial speed-ups can be obtained, while retaining a high resolution and precision of the results. Using the reduced-order model, the dominant frequency of a step response of the two-beam example model was successfully optimized to match a certain target frequency ω^⁎. One evaluation of the reduced-order model was on average 4.33 times faster than an evaluation of the full-order model. The optimum was successfully verified by the evaluation of the full-order model for the optimum design parameters which produced the same target frequency. This shows promise for the improvement of classical optimization approaches using reduced-order models also for different problem types.