Hill T L, Cammarano A, Neild S A, Barton D A W
Department of Mechanical Engineering, University of Bristol, Bristol, BS8 1TR, UK.
School of Engineering, University of Glasgow, Glasgow, G12 8QQ, UK.
Proc Math Phys Eng Sci. 2017 Mar;473(2199):20160789. doi: 10.1098/rspa.2016.0789.
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.
非线性正常模式（NNMs）被广泛用作理解非线性系统强迫响应的工具。然而，NNM的当代定义还包含大量在系统受到强迫和阻尼时未观察到的动态行为。因此，只需少数NNM就能理解强迫动力学。本文首先展示了一个简单非线性系统的NNM可能产生的复杂性——强调了需要一种识别NNM重要性的方法。通过分析研究并结合能量论证，来深入理解将NNM与强迫响应联系起来的机制。这有助于深入了解哪些NNM与理解强迫动力学相关，哪些可以忽略。将NNM与模拟的强迫响应进行比较，以验证这些发现。
