Experimental Tracking of Limit-Point Bifurcations and Backbone Curves Using Control-Based Continuation
Control-based continuation (CBC) is a means of applying numerical continuation directly to a physical experiment for bifurcation analysis without the use of a mathematical model. CBC enables the detection and tracking of bifurcations directly, without the need for a post-processing stage as is often the case for more traditional experimental approaches. In this paper, we use CBC to directly locate limit-point bifurcations of a periodically forced oscillator and track them as forcing parameters are varied. Backbone curves, which capture the overall frequency-amplitude dependence of the system’s forced response, are also traced out directly. The proposed method is demonstrated on a single-degree-of-freedom mechanical system with a nonlinear stiffness characteristic. Results are presented for two configurations of the nonlinearity — one where it exhibits a hardening stiffness characteristic and one where it exhibits softening-hardening..
| Medienart: |
Artikel |
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| Erscheinungsjahr: |
2017 |
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| Erschienen: |
2017 |
| Enthalten in: |
Zur Gesamtaufnahme - volume:27 |
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| Enthalten in: |
International journal of bifurcation and chaos - 27(2017), 1 |
| Sprache: |
Englisch |
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| Beteiligte Personen: |
Renson, Ludovic [VerfasserIn] |
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| Links: |
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| BKL: |
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| doi: |
10.1142/S0218127417300026 |
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OLC1991261217 |
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| 520 | |a Control-based continuation (CBC) is a means of applying numerical continuation directly to a physical experiment for bifurcation analysis without the use of a mathematical model. CBC enables the detection and tracking of bifurcations directly, without the need for a post-processing stage as is often the case for more traditional experimental approaches. In this paper, we use CBC to directly locate limit-point bifurcations of a periodically forced oscillator and track them as forcing parameters are varied. Backbone curves, which capture the overall frequency-amplitude dependence of the system’s forced response, are also traced out directly. The proposed method is demonstrated on a single-degree-of-freedom mechanical system with a nonlinear stiffness characteristic. Results are presented for two configurations of the nonlinearity — one where it exhibits a hardening stiffness characteristic and one where it exhibits softening-hardening. | ||
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