High-quality measurement data is required to validate vibration predictions. In addition, measurement data is needed to experimentally determine model parameters or identify data-driven models.
Vibration measurement methods currently in use are based on linear theory. However, there are numerous causes of nonlinear relations between force and motion quantities in real-life structures, such as nonlinear kinematic relationships (e.g., large deformations), nonlinear material behavior (e.g., hyperelasticity, plasticity), multi-physical interaction (e.g., flow-structure interaction), or nonlinear boundary conditions (e.g., friction, play). In the presence of nonlinearities, the currently used methods provide erroneous results. Our research focuses on the development and application of new measurement methods that are suitable for nonlinear behavior.
A particular focus is placed on damping, which almost always has strongly nonlinear causes. Damping determines how large vibrations become in the resonance case, whether self-excited vibrations (e.g., flutter) can occur, and how quickly free vibrations ring down after a shock-type loading. The frictional, inherently nonlinear contact interactions in mechanical connections (screws, rivets, etc.) are responsible for a large part of the damping in aerospace applications.
At ILA, we develop the theory behind measurement methods and prototypically implement them in our vibration laboratory. Together with our industry partners, we investigate the industrial benefits of these methods and bridge the gap between academic research and industrial application.
Our basic research can be applied in various areas of engineering and in structures of different sizes, from aircraft to wind turbines to microelectromechanical sensors (MEMS). We are thus making an important contribution to developing structures, machines and systems that are lightweight and resource-efficient, while at the same time ensuring safe and fault-free operation. In addition, our research enables the development of new technologies that make targeted use of nonlinearities to achieve unprecedented performance.
A special feature of nonlinear systems is that several vibration states are equally possible for the same excitation conditions (e.g., frequency and amplitude of a sinusoidal excitation force). These states can also occur in isolation, i.e., completely detached from the quasi-linear behavior at low amplitudes. Only by measuring all possible states, one can obtain meaningful data for model identification and validation. State-of-the-art vibration measurement technology and our control-based methods enable the analysis of highly complex, nonlinear vibrations of structures and systems.
Near-resonant, nonlinear vibrations can be described and predicted using the concept of nonlinear modes. Precise knowledge of damping is particularly important for this purpose, as this determines how large the amplitudes will be in case of resonance. Our measurement methods allows us to determine the amplitude-dependent damping, natural frequency, and vibration modes accurately and robustly. Here, too, we use approaches from control engineering to suppress the unwanted feedback of the structure under investigation on the excitation system.
Vibration testing of very large structures such as wind turbines are very costly and, in some cases, practically impossible. An interesting alternative is to identify data-driven models of the substructures and predict the vibration behavior of the overall structure using dynamic substructuring. However, conventional methods for substructuring neglect nonlinearities. We develop novel approaches for dynamic substructuring using nonlinear, experimentally identified models.
Short video explaining our research
Dr. Maren Scheel explains our research on the occasion of the Bertha Benz Prize for her dissertation (only in German).
Selected publications
- Hippold, P., Kleyman, G., Woiwode, L., Wei, T., Müller, F., Schwingshackl, C., Scheel, M., Tatzko, S., & Krack, M. (2025). An iteration-free approach to excitation harmonization. Mechanical Systems and Signal Processing, 233, 112732. https://doi.org/10.1016/j.ymssp.2025.112732
- Krack, M., Brake, M., Schwingshackl, C., Gross, J., Hippold, P., Lasen, M., Dini, D., Salles, L., Matt, Shetty, D., Payne, C. A., Willner, K., Lengger, M., Khan, M., Ortiz, J., Najera-Flores, D., Kuether, R. J., Miles, P., Xu, C., et al. (2025). The Tribomechadynamics Research Challenge: Confronting blind predictions for the linear and nonlinear dynamics of a thin-walled jointed structure with measurement results. Mechanical Systems and Signal Processing. https://doi.org/10.1016/j.ymssp.2024.112016
- Hippold, P., Scheel, M., Renson, L., & Krack, M. (2024). Robust and fast backbone tracking via phase-locked loops. Mechanical Systems and Signal Processing. https://doi.org/10.1016/j.ymssp.2024.111670
- Woiwode, L., & Krack, M. (2024). Experimentally uncovering isolas via backbone tracking. Journal of Structural Dynamics. https://doi.org/10.25518/2684-6500.180
- Bhattu, A., Hermann, S., Jamia, N., Müller, F., Scheel, M., Schwingshackl, C., Özgüven, H. N., & Krack, M. (2024). Experimental analysis of the TRC benchmark system. Journal of Structural Dynamics. https://doi.org/10.25518/2684-6500.206
- Müller, F., Woiwode, L., Gross, J., Scheel, M., & Krack, M. (2022). Nonlinear damping quantification from phase-resonant tests under base excitation. Mechanical Systems and Signal Processing, 177, 109170. https://doi.org/10.1016/j.ymssp.2022.109170
- Schwarz, S., Kohlmann, L., Hartung, A., Gross, J., Scheel, M., & Krack, M. (2020). Validation of a Turbine Blade Component Test With Frictional Contacts by Phase-Locked-Loop and Force-Controlled Measurements. Journal of Engineering for Gas Turbines and Power, 142, Article 5. https://doi.org/10.1115/1.4044772
- Scheel, M., Weigele, T., & Krack, M. (2020). Challenging an experimental nonlinear modal analysis method with a new strongly friction-damped structure. Journal of Sound and Vibration, 485, 115580. https://doi.org/10.1016/j.jsv.2020.115580
- Scheel, M., Peter, S., Leine, R. I., & Krack, M. (2018). A phase resonance approach for modal testing of structures with nonlinear dissipation. Journal of Sound and Vibration, 435, 56–73. https://doi.org/10.1016/j.jsv.2018.07.010
Maren Scheel
Dr.-Ing.Group leader "Experimental vibration analysis"