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    Towards a network perspective on the nonlinear dynamics of mechanical structures
    (2026)
    Geier, Charlotte
    ;
    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.
    Publicationtype: Doctoral Thesis
      70  45
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    Ice-induced vibrations of vertical structures
    (2021-12-09)
    Ziemer, Gesa
    ;
    Hoffmann, Norbert
    Vertical structures exposed to drifting level ice can exhibit significant ice-induced vibrations. However, their fundamental physical process is not sufficiently understood to date. Therefore, novel model tests in ice have been conducted utilizing local pressure mapping techniques to assess the influence of local failure processes on the occurrence of ice-induced vibrations. Analysis of the acquired data reveals a significant impact of the relative velocity between ice and structure on the local failure and contact development. Based on this finding, a prediction method and a scaling approach are developed.
    Publicationtype: Doctoral Thesis
      195  304
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    Data-driven techniques for the nonlinear dynamics of mechanical structures
    (2020-11)
    Stender, Merten
    ;
    Hoffmann, Norbert
    In structural vibrations, several modeling approaches have helped to develop better, i.e. safer, less-vibrating, and more controllable designs for machines and structures. However, complex nonlinear vibrations of multi-physics, multi-component, and multi-scale systems still represent challenges to today’s identification and vibration prediction approaches. Particularly, damping and friction can play a crucial role for vibration mitigation while being inherently difficult to characterize, quantify, or even approximate. At the same time, the data sciences have become omnipresent not only in different fields of science but also in society. This thesis introduces a rigorous framework and discusses chances and limitations for using machine learning in complex structural dynamics. Special focus is put on the physical peculiarities of the vibration signals and physics-informed learning. In the context of case studies, new methodologies are presented for several systems ranging from single-degree-of-freedom oscillators to complete automotive disk brake systems.
    Publicationtype: Doctoral Thesis
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    Inducing predefined nonlinear rogue waves on basis of breather solutions
    (2019)
    Witt, Andy
    ;
    Hoffmann, Norbert
    The Peregrine Breather, an analytical solution of the Nonlinear Schroedinger Equation, is modified to induce locally and temporally accurate, predefined extreme wave events in an arbitrary directed sea state. To this end, a parameter study of the distortion term of the unstable Peregrine modulation is performed to enforce form, height, and steepness of the rogue wave. In addition, the phase modulation is identified to be the crucial perturbation for the nonlinear Breather dynamic. With this knowledge, the inducing of a predefined rogue wave in non-uniform carrier waves and even in irregular, directed sea states is presented, its limits determined, and the Breather dynamics analyzed by spectral and phase evolution analysis in time and space. The results are compared to the dynamics of real occurred extreme waves and a reverse engineering as well as a forecast model for nonlinear real rogue waves are depicted briefly.
    Publicationtype: Doctoral Thesis
      596  550