Identifying the significance of nonlinear normal modes.
Identifying the significance of nonlinear normal modes.
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DOI：
10.1098/rspa.2016.0789
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发表时间：
2017-03
期刊：
影响因子：
--
通讯作者：
Barton DAW
中科院分区：
文献类型：
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作者：
Hill TL;Cammarano A;Neild SA;Barton DAW
非线性简正模态是研究非线性系统强迫响应的重要工具。然而，NNM的当代定义还包括大量的动态行为，这些行为在系统受力和阻尼时无法观察到。因此，只需要几个NNM就可以理解受迫动力学。本文首先证明了复杂性，可能会出现一个简单的非线性系统的NNMs突出需要一种方法来识别NNMs的意义。一个分析调查，能源参数，开发一个了解的机制，相关的NNMs的强制响应。这提供了洞察哪些NNM与理解强迫动力学有关，哪些可以被忽略。NNMs与模拟的强迫响应进行比较，以验证这些发现。
Nonlinear normal modes (NNMs) are widely used as a tool for understanding the forced responses of nonlinear systems. However, the contemporary definition of an NNM also encompasses a large number of dynamic behaviours which are not observed when a system is forced and damped. As such, only a few NNMs are required to understand the forced dynamics. This paper firstly demonstrates the complexity that may arise from the NNMs of a simple nonlinear system—highlighting the need for a method for identifying the significance of NNMs. An analytical investigation is used, alongside energy arguments, to develop an understanding of the mechanisms that relate the NNMs to the forced responses. This provides insight into which NNMs are pertinent to understanding the forced dynamics, and which may be disregarded. The NNMs are compared with simulated forced responses to verify these findings.