The influence of phase-locking on internal resonance from a nonlinear normal mode perspective

Hill, T.L., Neild, S.A., Cammarano, A. and Wagg, D.J. (2016) The influence of phase-locking on internal resonance from a nonlinear normal mode perspective. Journal of Sound and Vibration, 379, pp. 135-149. (doi:10.1016/j.jsv.2016.05.028)

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Abstract

When a nonlinear system is expressed in terms of the modes of the equivalent linear system, the nonlinearity often leads to modal coupling terms between the linear modes. In this paper it is shown that, for a system to exhibit an internal resonance between modes, a particular type of nonlinear coupling term is required. Such terms impose a phase condition between linear modes, and hence are denoted phase-locking terms. The effect of additional modes that are not coupled via phase-locking terms is then investigated by considering the backbone curves of the system. Using the example of a two-mode model of a taut horizontal cable, the backbone curves are derived for both the case where phase-locked coupling terms exist, and where there are no phase-locked coupling terms. Following this, an analytical method for determining stability is used to show that phase-locking terms are required for internal resonance to occur. Finally, the effect of non-phase-locked modes is investigated and it is shown that they lead to a stiffening of the system. Using the cable example, a physical interpretation of this is provided.

Item Type:Articles
Additional Information:The authors would like to acknowledge the support from the Engineering and Physical Sciences Research Council. S.A.N. and T.L.H. are supported by EP/K005375/1 and D.J.W. is supported by EP/K003836/1.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Cammarano, Dr Andrea
Authors: Hill, T.L., Neild, S.A., Cammarano, A., and Wagg, D.J.
College/School:College of Science and Engineering > School of Engineering > Systems Power and Energy
Journal Name:Journal of Sound and Vibration
Publisher:Elsevier
ISSN:0022-460X
Published Online:06 June 2016
Copyright Holders:Copyright © 2016 The Authors
First Published:First published in Journal of Sound and Vibration 379: 135-149
Publisher Policy:Reproduced under a Creative Commons License

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