Control-based continuation for investigating nonlinear experiments
Control-based continuation for investigating nonlinear experiments
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DOI：
10.1177/1077546310384004
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发表时间：
2012-04-01
影响因子：
2.8
通讯作者：
Burrow, Stephen G.
中科院分区：
文献类型：
--
作者：
Barton, David A. W.;Mann, Brian P.;Burrow, Stephen G.
在本文中，我们提出了一个系统的实验研究，两个一个自由度的非线性装置使用新引入的基于控制的连续方法Sieber和Krauskopf。通过考虑硬化，软化和弹簧特性，我们证明了多功能性和电源的控制为基础的连续方法进行调查的非线性实验。我们表明，使用这种方法，它是可能的跟踪稳定轨道的设备通过鞍结分岔（倍），他们失去稳定性，并继续他们的共振峰，他们经历了第二个鞍结分岔。对于非线性情况，产生了一个分叉图，它强烈地让人想起使用经典谐波平衡解产生的分叉图。一般延续方法的详细介绍，包括使其他实验者实施。
In this paper we present a systematic experimental study of two one-degree-of-freedom nonlinear devices using the newly introduced control-based continuation method of Sieber and Krauskopf. By considering hardening, softening and bistable spring characteristics, we demonstrate the versatility and power of the control-based continuation method for investigating nonlinear experiments. We show that, using this method, it is possible to track the stable orbits of the devices through a saddle-node bifurcation (fold) where they lose stability and continue them up to the resonance peak where they undergo a second saddle-node bifurcation. For the bistable case, a bifurcation diagram is produced that is strongly reminiscent of the bifurcation diagram produced using the classical harmonic balance solution. A detailed introduction to general continuation methods is included to enable implementation by other experimentalists.