Efficient model order reduction for the nonlinear dynamics of jointed structures by the use of trial vector derivatives

The dynamic response of a structure, which consists of jointed substructures, may be influenced by the nonlinear contact and friction forces inside the joints, even if the deformations are small. In case of joints with a large spatial distribution, like in car bodies or leaf springs, these nonlinearities dominate the overall system behavior. The use of the direct finite element method or a standard model order reduction technique leads to either huge computational costs or inaccurate results. So called ‘Joint Interface Modes’ (JIMs) overcome that problem. They represent a problem oriented extension of classical trial vectors for structures with bolted joints, spot welded seems and similar joints. The result quality is comparable to that one of a direct finite element analysis without losing the efficiency of model order reduction. In this paper a new approach for the computation of such JIMs is presented. The approach is based on so called trial vector derivatives which will be outlined in the theory part of the paper. At the end of the paper, the theory is applied to a static and dynamic example in order to underline the methods accuracy and efficiency.