Bifurcations of backbone curves for systems of coupled nonlinear two mass oscillator
Bifurcations of backbone curves for systems of coupled nonlinear two mass oscillator
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DOI：
10.1007/s11071-014-1295-3
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发表时间：
2014-07-01
影响因子：
5.6
通讯作者：
Wagg, D. J.
中科院分区：
文献类型：
--
作者：
Cammarano, A.;Hill, T. L.;Wagg, D. J.
本文研究了两自由度耦合受迫轻阻尼型非线性振子的动力响应。对于这些系统，主干曲线定义了频率-位移平面上的共振峰，并为预测系统的频率响应提供了有价值的信息。此前，已有研究表明，主干曲线中可能会出现分叉。在这篇文章中，我们提出了一种分析方法，使我们能够识别这种分叉发生的条件。这种基于二阶非线性规范形的方法还能够提供有关分叉的性质以及它们如何影响响应特性的信息。该方法被应用于具有立方硬化弹簧的两自由度质量、弹簧、阻尼器系统。我们使用二阶规范形法对系统坐标进行变换，识别哪些参数值会导致主干曲线的共振相互作用和分叉。此外，还给出了主干曲线与强迫系统复杂动力学之间的关系。
This paper considers the dynamic response of coupled, forced and lightly damped nonlinear oscillators with two degree-of-freedom. For these systems, backbone curves define the resonant peaks in the frequency-displacement plane and give valuable information on the prediction of the frequency response of the system. Previously, it has been shown that bifurcations can occur in the backbone curves. In this paper, we present an analytical method enabling the identification of the conditions under which such bifurcations occur. The method, based on second-order nonlinear normal forms, is also able to provide information on the nature of the bifurcations and how they affect the characteristics of the response. This approach is applied to a two-degree-of-freedom mass, spring, damper system with cubic hardening springs. We use the second-order normal form method to transform the system coordinates and identify which parameter values will lead to resonant interactions and bifurcations of the backbone curves. Furthermore, the relationship between the backbone curves and the complex dynamics of the forced system is shown.