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 of 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 vibration frequency of the two-beams 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 analysis also shows that the reduced-order model based optimum design matches the target frequency ω* very well. This optimum was succesfully 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.