Identifying the significance of nonlinear normal modes
Identifying the significance of nonlinear normal modes
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.
Hill, T.L.
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Cammarano, A.
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Neild, S.A.
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Barton, D.A.W.
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31 March 2017
Hill, T.L.
96922dda-e993-4889-a519-5f89fe6ebca8
Cammarano, A.
c0c85f55-3dfc-4b97-9b79-e2554406a12b
Neild, S.A.
e11b68bb-ddff-4cac-a8a7-798cc3cc3891
Barton, D.A.W.
3003bb1f-d648-4d00-a309-8ab75f333df0
Hill, T.L., Cammarano, A., Neild, S.A. and Barton, D.A.W.
(2017)
Identifying the significance of nonlinear normal modes.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473 (2199).
(doi:10.1098/rspa.2016.0789).
Abstract
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.
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hill-et-al-2017-identifying-the-significance-of-nonlinear-normal-modes
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Accepted/In Press date: 27 January 2017
e-pub ahead of print date: 1 March 2017
Published date: 31 March 2017
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Local EPrints ID: 490781
URI: http://eprints.soton.ac.uk/id/eprint/490781
ISSN: 1364-5021
PURE UUID: 188b8f6e-4ab3-4bfb-abdd-f8c65cef0f60
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Date deposited: 06 Jun 2024 16:42
Last modified: 07 Jun 2024 02:08
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Author:
T.L. Hill
Author:
A. Cammarano
Author:
S.A. Neild
Author:
D.A.W. Barton
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