Hoffmann, Norbert

The nonlinear dynamics of mechanical structures present significant challenges in engineering today, particularly as these structures become more intricate and environmental conditions grow increasingly unpredictable. In this work, different perspectives on the dynamics of mechanical structures are explored and compared. The balance between interpretability and generalizability is studied in the context of classical, physics-based approaches, data-driven methods and new network-based techniques. Network science offers novel views by interpreting mechanical systems as networks composed of nodes and edges. This thesis focusses on the applicability and potential of network-based methods for analyzing mechanical structures.

Vibrations in braking systems have been studied since the beginning of the last century and despite several insights, still many phenomena, particularly in the area of friction induced vibrations, are not fully understood. The objective of the actual study was the identification of the complex dynamics in the friction interface of a dry friction brake system. In this context, particular consideration was given to the generation of instabilities and brake squeal. In work presently being undertaken, irregular vibration data of a dry friction brake in non-squealing condition were collected with sampling rates above 200 kHz. The resulting time series were subjected to linear, nonlinear and statistical analyses and in particular with regard to the involved multi-scale dynamics. At first, topological examination of the friction surfaces disclosed the microscale characteristics; visual inspections of the coating, generated on the brake disk insights in to the friction interface transformations. Secondly, linear investigations of the vibration data in the frequency domain provided first impressions of the friction interface: while the spectral frequency distribution remains mostly independent from mechanic parameters, it is essentially controlled by the pad formulation and physical and chemical interface transformations during the experiment. Thirdly, the data were explored on the basis of recurrence analysis and together with the estimation of dimensionality the phase space was reconstructed. Evidently, the irregular vibration states of friction brakes in non-squealing condition are strongly controlled both by apparently steady and disruptive phenomena (intermittency). The duration between the states was typically in the range of milliseconds. Phase space reconstruction and largest Lyapunov coefficient estimation indicated thereby that these phenomena are dominated more by low-dimensional chaotic deterministic dynamics than by high-dimensional stochastic processes. In the following, characteristic measures of the recurrence quantification analysis have been extracted which disclosed an interrelation with the noise propensity of the overall brake system. Finally, statistical studies of the distribution of vibration increments on the basis of probability density functions concluded the evaluation of the experiments. The distribution analyses disclosed the non-Gaussian characteristic of the vibration signals under steady sliding whereby the deviation from the normal distribution depends on the corresponding scale. Furthermore, the vibration during sliding in non-squealing condition is effectively generated by dynamics on different scales. And beyond that, the difference between the measured and the Gaussian distribution suggests a correlation between the squeal propensity and the deviation under consideration.

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