The Significance of Nonlinear Normal Modes for Forced Responses

Hill, T.L., Neild, S.A., Cammarano, A. and Barton, D.A.W. (2017) The Significance of Nonlinear Normal Modes for Forced Responses. In: Proceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics 2017, Garden Grove, CA, USA, 30 Jan - 02 Feb 2017, pp. 135-142. ISBN 9783319455038 (doi:10.1007/978-3-319-54404-5_14)

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Abstract

Nonlinear normal modes (NNMs) describe the unforced and undamped periodic responses of nonlinear systems. NNMs have proven to be a valuable tool, and are widely used, for understanding the underlying behaviour of nonlinear systems. They provide insight into the types of behaviour that may be observed when a system is subjected to forcing and damping, which is ultimately of primary concern in many engineering applications. The definition of an NNM has seen a number of evolutions, and the contemporary definition encompasses all periodic responses of a conservative system. Such a broad definition is essential, as it allows for the wide variety of responses that nonlinear systems may exhibit. However, it may also lead to misleading results, as some of the NNMs of a system may represent behaviour that will only be observed under very specific forcing conditions, which may not be realisable in any practical scenario. In this paper, we investigate how the significance of NNMs may differ and how this significance may be quantified. This is achieved using an energy-based method, and is validated using numerical simulations.

Item Type:Conference Proceedings
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Cammarano, Dr Andrea
Authors: Hill, T.L., Neild, S.A., Cammarano, A., and Barton, D.A.W.
College/School:College of Science and Engineering > School of Engineering > Systems Power and Energy
ISSN:2191-5644
ISBN:9783319455038
Published Online:04 May 2017
Copyright Holders:Copyright © 2017 The Society for Experimental Mechanics, Inc.
First Published:First published in Nonlinear Dynamics, Volume 1: 135-142
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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