Developing complex network perspectives as an alternative view on nonlinear dynamics in large multi-component mechanical structures - Towards a better understanding of engineering vibrations

• Applicant: Professor Dr. Norbert Hoffmann
• Subject Area: Mechanics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 510246309

This project aims at integrating methods from the field of complex networks into the analysis of large multi-component mechanical structures and their dynamics. Complex network analysis is a growing field of research that is applied throughout many different disciplines such as medicine, earth sciences or fluid dynamics. We propose a novel way of approaching current challenges in mechanical systems analysis by complementing the classical view of a geometric structure with a functional network perspective: The structure is represented as a network of individual components, and hence one can study the dynamic interplay, driving agents and component roles in the overall system dynamics better than with traditional methods. With the tools of network analysis, current challenges in nonlinear engineering dynamics can be handled in new and simpler ways. Particularly, the outcome of this project will allow for (i) visualization of dynamical phenomena hidden in the high dimensionality of the system; (ii) identification of emergent phenomena arising from collective behavior; (iii) analysis and design of mechanical system improved by network analysis tools. A network-based view on structural dynamics will enable us to identify and predict qualitative changes in the systems behavior, such as bifurcations, and emergent phenomena. Functional network representations of the complex dynamical system will provide a more intuitive understanding of the system dynamics, its governing nonlinearities and dynamic relationships between the components and sub-assemblies. This viewpoint will be expedient in the development of new multi-component mechanical systems, as resources can be focused on the dynamically most relevant parts during the design process. The methods obtained throughout this project will be of use for manufacturing and and quality management, when defining manufacturing tolerances or assessing fault impacts. Early warning methods for transitions and rare events can be established based on the proposed complex network analysis, which are of special interest in predictive maintenance. Thus, all phases of a products life cycle can profit from a complex network perspective on the systems dynamics rendered accessible through this project.

• DFG Programme: Research Grants
• Co-Investigator: Professor Dr.-Ing. Merten Stender