Relating Backbone Curves to the Forced Responses of Nonlinear Systems

Tom L Hill; Andrea Cammarano; Simon A Neild; David J Wagg

doi:10.1007/978-3-319-15221-9_9

Relating Backbone Curves to the Forced Responses of Nonlinear Systems

Tom L Hill, Andrea Cammarano, Simon A Neild, David J Wagg

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

2 Citations (Scopus)

354 Downloads (Pure)

Abstract

Backbone curves describe the steady-state responses of unforced, undamped systems, therefore they do not directly relate to any specific forcing and damping configuration. Nevertheless, they can be used to understand the underlying dynamics of nonlinear systems subjected to forcing and damping. Building on this concept, in this paper we describe an analytical technique used to predict the onset of internally-resonant modal interactions in an example system. In conjunction with backbone curve analysis, which can be used to predict the possibility of internally-resonant behaviour, this approach provides an analytical tool for understanding and quantifying internally-resonant regions in the forced responses.

Original language	English
Title of host publication	Nonlinear Dynamics, Volume 1
Subtitle of host publication	Proceedings of the 33rd IMAC, A Conference and Exposition on Structural Dynamics, 2015
Editors	Gaëtan Kerschen
Publisher	Springer
Pages	113-122
Number of pages	10
ISBN (Electronic)	9783319152219
ISBN (Print)	9783319152202
DOIs	https://doi.org/10.1007/978-3-319-15221-9_9
Publication status	Published - 14 Aug 2015
Event	33rd IMAC Conference and Exposition on Structural Dynamics, 2015 - Orlando, FL, United States Duration: 2 Feb 2015 → 5 Feb 2015

Publication series

Name	Conference Proceedings of the Society for Experimental Mechanics Series
Publisher	Springer
ISSN (Print)	2191-5644

Conference

Conference	33rd IMAC Conference and Exposition on Structural Dynamics, 2015
Country/Territory	United States
City	Orlando, FL
Period	2/02/15 → 5/02/15

Keywords

Backbone curves
Second-order normal forms
Modal analysis
Modal interaction
Modal reduction

Access to Document

10.1007/978-3-319-15221-9_9

IMAC2015_dft_06
This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Springer at http://link.springer.com/chapter/10.1007%2F978-3-319-15221-9_9. Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 311 KB

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Dynamic design tools for understanding and exploiting nonlinearity in structures
Neild, S. A.
1/02/13 → 31/07/18
Project: Research

Cite this

Hill, T. L., Cammarano, A., Neild, S. A., & Wagg, D. J. (2015). Relating Backbone Curves to the Forced Responses of Nonlinear Systems. In G. Kerschen (Ed.), Nonlinear Dynamics, Volume 1: Proceedings of the 33rd IMAC, A Conference and Exposition on Structural Dynamics, 2015 (pp. 113-122). (Conference Proceedings of the Society for Experimental Mechanics Series). Springer. https://doi.org/10.1007/978-3-319-15221-9_9

Hill, Tom L ; Cammarano, Andrea ; Neild, Simon A et al. / Relating Backbone Curves to the Forced Responses of Nonlinear Systems. Nonlinear Dynamics, Volume 1: Proceedings of the 33rd IMAC, A Conference and Exposition on Structural Dynamics, 2015. editor / Gaëtan Kerschen. Springer, 2015. pp. 113-122 (Conference Proceedings of the Society for Experimental Mechanics Series).

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title = "Relating Backbone Curves to the Forced Responses of Nonlinear Systems",

abstract = "Backbone curves describe the steady-state responses of unforced, undamped systems, therefore they do not directly relate to any specific forcing and damping configuration. Nevertheless, they can be used to understand the underlying dynamics of nonlinear systems subjected to forcing and damping. Building on this concept, in this paper we describe an analytical technique used to predict the onset of internally-resonant modal interactions in an example system. In conjunction with backbone curve analysis, which can be used to predict the possibility of internally-resonant behaviour, this approach provides an analytical tool for understanding and quantifying internally-resonant regions in the forced responses.",

keywords = "Backbone curves, Second-order normal forms, Modal analysis, Modal interaction, Modal reduction",

author = "Hill, {Tom L} and Andrea Cammarano and Neild, {Simon A} and Wagg, {David J}",

year = "2015",

month = aug,

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language = "English",

isbn = "9783319152202",

series = "Conference Proceedings of the Society for Experimental Mechanics Series",

publisher = "Springer",

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note = "33rd IMAC Conference and Exposition on Structural Dynamics, 2015 ; Conference date: 02-02-2015 Through 05-02-2015",

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Hill, TL, Cammarano, A, Neild, SA & Wagg, DJ 2015, Relating Backbone Curves to the Forced Responses of Nonlinear Systems. in G Kerschen (ed.), Nonlinear Dynamics, Volume 1: Proceedings of the 33rd IMAC, A Conference and Exposition on Structural Dynamics, 2015. Conference Proceedings of the Society for Experimental Mechanics Series, Springer, pp. 113-122, 33rd IMAC Conference and Exposition on Structural Dynamics, 2015, Orlando, FL, United States, 2/02/15. https://doi.org/10.1007/978-3-319-15221-9_9

Relating Backbone Curves to the Forced Responses of Nonlinear Systems. / Hill, Tom L; Cammarano, Andrea; Neild, Simon A et al.

Nonlinear Dynamics, Volume 1: Proceedings of the 33rd IMAC, A Conference and Exposition on Structural Dynamics, 2015. ed. / Gaëtan Kerschen. Springer, 2015. p. 113-122 (Conference Proceedings of the Society for Experimental Mechanics Series).

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

TY - GEN

T1 - Relating Backbone Curves to the Forced Responses of Nonlinear Systems

AU - Hill, Tom L

AU - Cammarano, Andrea

AU - Neild, Simon A

AU - Wagg, David J

PY - 2015/8/14

Y1 - 2015/8/14

N2 - Backbone curves describe the steady-state responses of unforced, undamped systems, therefore they do not directly relate to any specific forcing and damping configuration. Nevertheless, they can be used to understand the underlying dynamics of nonlinear systems subjected to forcing and damping. Building on this concept, in this paper we describe an analytical technique used to predict the onset of internally-resonant modal interactions in an example system. In conjunction with backbone curve analysis, which can be used to predict the possibility of internally-resonant behaviour, this approach provides an analytical tool for understanding and quantifying internally-resonant regions in the forced responses.

AB - Backbone curves describe the steady-state responses of unforced, undamped systems, therefore they do not directly relate to any specific forcing and damping configuration. Nevertheless, they can be used to understand the underlying dynamics of nonlinear systems subjected to forcing and damping. Building on this concept, in this paper we describe an analytical technique used to predict the onset of internally-resonant modal interactions in an example system. In conjunction with backbone curve analysis, which can be used to predict the possibility of internally-resonant behaviour, this approach provides an analytical tool for understanding and quantifying internally-resonant regions in the forced responses.

KW - Backbone curves

KW - Second-order normal forms

KW - Modal analysis

KW - Modal interaction

KW - Modal reduction

U2 - 10.1007/978-3-319-15221-9_9

DO - 10.1007/978-3-319-15221-9_9

M3 - Conference Contribution (Conference Proceeding)

SN - 9783319152202

T3 - Conference Proceedings of the Society for Experimental Mechanics Series

SP - 113

EP - 122

BT - Nonlinear Dynamics, Volume 1

A2 - Kerschen, Gaëtan

PB - Springer

T2 - 33rd IMAC Conference and Exposition on Structural Dynamics, 2015

Y2 - 2 February 2015 through 5 February 2015

ER -

Hill TL, Cammarano A, Neild SA, Wagg DJ. Relating Backbone Curves to the Forced Responses of Nonlinear Systems. In Kerschen G, editor, Nonlinear Dynamics, Volume 1: Proceedings of the 33rd IMAC, A Conference and Exposition on Structural Dynamics, 2015. Springer. 2015. p. 113-122. (Conference Proceedings of the Society for Experimental Mechanics Series). https://doi.org/10.1007/978-3-319-15221-9_9

Relating Backbone Curves to the Forced Responses of Nonlinear Systems

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Dynamic design tools for understanding and exploiting nonlinearity in structures

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