Identifying the significance of nonlinear normal modes

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 of London Series A: Mathematical, Physical and Engineering Sciences, 473(2199), 20160789. (doi:10.1098/rspa.2016.0789) (PMID:28413342) (PMCID:PMC5378240)

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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.

Item Type:Articles
Keywords:Backbone curves, energy transfer, nonlinear normal modes, resonance, second-order normal form technique, structural dynamics.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Cammarano, Dr Andrea
Authors: Hill, T.L., Cammarano, A., Neild, S.A., and Barton, D.A.W.
College/School:College of Science and Engineering > School of Engineering > Systems Power and Energy
Journal Name:Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences
Publisher:The Royal Society
ISSN:1364-5021
ISSN (Online):1471-2946
Published Online:01 March 2017
Copyright Holders:Copyright © 2017 The Authors
First Published:First published in Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences 473(2199):20160789
Publisher Policy:Reproduced under a Creative Commons License

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