Kraus, Zacharias Johannes (2024)
Robust stabilization and anti-resonance in parametrically excited dynamical systems.
Technische Universität Darmstadt
doi: 10.26083/tuprints-00027801
Dissertation, Erstveröffentlichung, Verlagsversion
Kurzbeschreibung (Abstract)
The excitation of dynamic systems through time-periodic changes of system parameters, also known as parametric excitation, has recently proven to allow for stabilization of solutions. The phenomenon used for this purpose is referred to as anti-resonance. It has primarily been described in the past by the change of the largest Lyapunov characteristic exponent (LCE). Regarding the underlying working principle, it is speculated that the systems' damping can be better utilized due to an energy exchange between vibration modes.
The aim of this work is a comprehensive understanding of stabilization through parametric excitation and the conditions necessary for its occurrence. For this purpose, three new perspectives are introduced. Firstly, it becomes apparent that for the characterization of all resonance effects, all LCEs are needed instead of just the largest one. Using this, the influences of circulatory and gyroscopic terms, as well as the phase relationships between excitation terms, are phenomenologically demonstrated. Secondly, in an energy consideration, a virtual dissipation is introduced to investigate the assumptions regarding the working principle. The evaluation of the derived expression shows that anti-resonance causes not only stabilization but also destabilization. This contradicts the previously common assumption that anti-resonance is a stabilizing phenomenon. To clarify the influence of parametric resonances, in the third step, an energy difference between the excited and unexcited systems is introduced and analytically derived. It becomes clear that the observed effects are based on a complex interplay of the work of damping and parametric excitation terms. Moreover, the stabilization of solutions with certain initial conditions always comes at the expense of destabilizing others. The analytical results are experimentally validated on two coupled micro-cantilevers.
The results lead to questioning the aptitude of the LCEs to assess parametric excitation, as they do not encompass the influence of all critical factors. Furthermore, it becomes apparent that a differentiated analysis is necessary for evaluating stabilization effects caused by parametric excitation. For this purpose, the internal energy difference introduced in this work proves to be excellently suited.
| Typ des Eintrags: | Dissertation | ||||
|---|---|---|---|---|---|
| Erschienen: | 2024 | ||||
| Autor(en): | Kraus, Zacharias Johannes | ||||
| Art des Eintrags: | Erstveröffentlichung | ||||
| Titel: | Robust stabilization and anti-resonance in parametrically excited dynamical systems | ||||
| Sprache: | Englisch | ||||
| Referenten: | Hagedorn, Prof. Dr. Peter ; Schweizer, Prof. Dr. Bernhard ; Dohnal, Prof. Dr. Fadi | ||||
| Publikationsjahr: | 30 August 2024 | ||||
| Ort: | Darmstadt | ||||
| Kollation: | x, 132 Seiten | ||||
| Datum der mündlichen Prüfung: | 26 Juni 2024 | ||||
| DOI: | 10.26083/tuprints-00027801 | ||||
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/27801 | ||||
| Kurzbeschreibung (Abstract): | The excitation of dynamic systems through time-periodic changes of system parameters, also known as parametric excitation, has recently proven to allow for stabilization of solutions. The phenomenon used for this purpose is referred to as anti-resonance. It has primarily been described in the past by the change of the largest Lyapunov characteristic exponent (LCE). Regarding the underlying working principle, it is speculated that the systems' damping can be better utilized due to an energy exchange between vibration modes. The aim of this work is a comprehensive understanding of stabilization through parametric excitation and the conditions necessary for its occurrence. For this purpose, three new perspectives are introduced. Firstly, it becomes apparent that for the characterization of all resonance effects, all LCEs are needed instead of just the largest one. Using this, the influences of circulatory and gyroscopic terms, as well as the phase relationships between excitation terms, are phenomenologically demonstrated. Secondly, in an energy consideration, a virtual dissipation is introduced to investigate the assumptions regarding the working principle. The evaluation of the derived expression shows that anti-resonance causes not only stabilization but also destabilization. This contradicts the previously common assumption that anti-resonance is a stabilizing phenomenon. To clarify the influence of parametric resonances, in the third step, an energy difference between the excited and unexcited systems is introduced and analytically derived. It becomes clear that the observed effects are based on a complex interplay of the work of damping and parametric excitation terms. Moreover, the stabilization of solutions with certain initial conditions always comes at the expense of destabilizing others. The analytical results are experimentally validated on two coupled micro-cantilevers. The results lead to questioning the aptitude of the LCEs to assess parametric excitation, as they do not encompass the influence of all critical factors. Furthermore, it becomes apparent that a differentiated analysis is necessary for evaluating stabilization effects caused by parametric excitation. For this purpose, the internal energy difference introduced in this work proves to be excellently suited. |
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| Alternatives oder übersetztes Abstract: |
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| Status: | Verlagsversion | ||||
| URN: | urn:nbn:de:tuda-tuprints-278019 | ||||
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften und Maschinenbau | ||||
| Fachbereich(e)/-gebiet(e): | 16 Fachbereich Maschinenbau 16 Fachbereich Maschinenbau > Dynamik und Schwingungen |
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| TU-Projekte: | DFG|HA1060/60-1|Robuste Stabilisieru | ||||
| Hinterlegungsdatum: | 30 Aug 2024 09:14 | ||||
| Letzte Änderung: | 02 Sep 2024 05:12 | ||||
| PPN: | |||||
| Referenten: | Hagedorn, Prof. Dr. Peter ; Schweizer, Prof. Dr. Bernhard ; Dohnal, Prof. Dr. Fadi | ||||
| Datum der mündlichen Prüfung / Verteidigung / mdl. Prüfung: | 26 Juni 2024 | ||||
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