Nonlinear Dynamic Substructuring of Thin-Walled Jointed Structures

• Applicant: Professor Dr.-Ing. Malte Krack
• Subject Area: Mechanics
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 450056469

This project addresses assemblies of thin-walled structures such as systems of external skin panels of wings and fuselage of airplanes and helicopters or space structures. Lightweight design has made these structures susceptible to vibration problems. The vibration behavior is characterized by two types of nonlinearities: Geometric nonlinearities arise due to bending-stretching coupling and become already relevant as soon as the bending deformation is in the range of the thickness. Contact nonlinearities arise due to dry frictional and unilateral interactions e.g. in riveted or bolted joints. Both geometric and contact nonlinearity cause a strong amplitude dependence of the effective stiffness distribution. This, in turn, has a substantial effect on the natural frequencies and the vibration stresses. Moreover, the frictional contact interactions are responsible for the largest part of the mechanical damping. Finally, either nonlinearity has the potential to trigger strongly nonlinear phenomena, such as the occurrence of new resonances. Thus, both nonlinearities are crucial for the accurate prediction of the forced vibration response and the behavior in the presence of self-excitation.The goals of this project are to (a) develop an efficient computational method for the nonlinear vibration analysis of thin-walled jointed structures, (b) assess the prediction accuracy of this method using appropriate experiments, and (c) understand the interactions between geometric and contact nonlinearities.To reach a high prediction accuracy, method will properly account for both geometric and contact nonlinearities.To achieve high computational efficiency, a drastic reduction of the mathematical model order will be pursued by a stepwise dynamic substructuring approach. Here, consistent use will be made of component mode synthesis and interface reduction methods, taking into account the specific properties of each substructure. The performance of the method will be assessed for both broadband and periodic excitation. For the special but technically relevant case of periodic near-resonant forcing, a further reduction based on the concept of nonlinear modes of vibration will be developed and assessed. It is expected that the method to be developed in this project reduces the computational effort for the described nonlinear vibration analyses by at least three orders of magnitude, compared to the available finite element tools. Finally, experimental investigations are carried out in order to thoroughly assess the validity of the developed approach.Today, engineering design relies on linear theory almost everywhere. Thus, nonlinearities are seen as the main reason for the lacking prediction accuracy in the state-of-the-art modeling strategies. The proposed project will make a substantial contribution to predictively modeling assemblies of lightweight structures. Only with predictive models, radically improved technology can be developed.

• DFG Programme: Research Grants