Application of control-based continuation to a nonlinear structure with harmonically coupled modes
Application of control-based continuation to a nonlinear structure with harmonically coupled modes
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DOI：
10.1016/j.ymssp.2018.10.008
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发表时间：
2018-07
影响因子：
8.4
通讯作者：
L. Renson;A. Shaw;D. Barton;S. Neild
中科院分区：
文献类型：
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作者：
L. Renson;A. Shaw;D. Barton;S. Neild
本文提出了一种探索多自由度物理实验非线性动力学的系统方法。为了说明这种基于控制的延拓(CBC)方法的有效性，将其应用于一个非线性梁结构，该结构的前两个弯曲振型之间呈现出3：1的强耦合模式。CBC可以直接从实验中提取包括ISOLA在内的一系列动力学特征，而不需要借助模型拟合或其他间接数据处理方法。这是第一次在存在复杂的多自由度响应特征的情况下的CBC的实验演示，例如内共振、Isola和Neimark-Sacker分叉。在本文中，我们证明了在单自由度系统中使用的反馈控制方法和路径跟踪技术同样可以应用于多自由度系统。首先将低电平宽带激励应用于实验，以获得控制器设计所需的信息，然后将物理实验视为使用CBC进行探测的“黑匣子”。对所用控制器的侵入性进行了分析，并通过开环测量验证了实验结果。在开环和闭环结果之间达到了很好的一致性，尽管发现在处理施加到结构上的力中存在高次谐波时需要谨慎。
This paper presents a systematic method for exploring the nonlinear dynamics of multi-degree-of-freedom (MDOF) physical experiments. To illustrate the power of this method, known as control-based continuation (CBC), it is applied to a nonlinear beam structure that exhibits a strong 3:1 modal coupling between its first two bending modes. CBC is able to extract a range of dynamical features, including an isola, directly from the experiment without recourse to model fitting or other indirect data-processing methods.Previously, CBC has only been applied to (essentially) single-degree-of-freedom (SDOF) experiments. This is the first experimental demonstration of CBC in the presence of complex MDOF response features such as internal resonance, isola, and Neimark-Sacker bifurcations. In this paper we show that the feedback-control methods and path-following techniques used in a SDOF context can equally be applied to MDOF systems. A low-level broadband excitation is initially applied to the experiment to obtain the requisite information for controller design and, subsequently, the physical experiment is treated as a “black box” that is probed using CBC. The invasiveness of the controller used is analysed and experimental results are validated with open-loop measurements. Good agreement between open- and closed-loop results is achieved, though it is found that care needs to be taken in dealing with the presence of higher-harmonics in the force applied to the structure.