Experimental Tracking of Limit-Point Bifurcations and Backbone Curves Using Control-Based Continuation
Experimental Tracking of Limit-Point Bifurcations and Backbone Curves Using Control-Based Continuation
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DOI：
10.1142/s0218127417300026
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发表时间：
2017-02
期刊：
影响因子：
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通讯作者：
L. Renson;D. Barton;S. Neild
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文献类型：
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作者：
L. Renson;D. Barton;S. Neild
基于控制的延拓（CBC）是一种不使用数学模型，直接将数值延拓应用于物理实验进行分岔分析的方法。CBC可以直接检测和跟踪分岔，而不需要像传统实验方法那样进行后处理阶段。本文利用CBC直接定位周期性强迫振荡器的极限点分岔，并在强迫参数变化时对其进行跟踪。捕获系统强迫响应的总体频率-幅度依赖关系的主干曲线也被直接追踪出来。在具有非线性刚度特性的单自由度机械系统上进行了验证。结果提出了非线性的两种配置-一种是它表现出硬化刚度特性，另一种是它表现出软化硬化。
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.