Simplifying Transformations for Nonlinear Systems: Part I, An Optimisation-Based Variant of Normal Form Analysis

N Dervilis; Keith Worden; David J Wagg; Simon A Neild

doi:10.1007/978-3-319-15221-9_28

Simplifying Transformations for Nonlinear Systems: Part I, An Optimisation-Based Variant of Normal Form Analysis

N Dervilis, Keith Worden, David J Wagg, Simon A Neild

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

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Abstract

This paper introduces the idea of a ‘simplifying transformation’ for nonlinear structural dynamic systems. The idea simply stated; is to bring under one heading, those transformations which ‘simplify’ structural dynamic systems or responses in some sense. The equations of motion may be cast in a simpler form or decoupled (and in this sense, nonlinear modal analysis is encompassed) or the responses may be modified in order to isolate and remove certain components. It is the latter sense of simplification which is considered in this paper. One can regard normal form analysis in a way as the removal of superharmonic content from nonlinear system response. In the current paper, this problem is cast in an optimisation form and the differential evolution algorithm is used.

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	315-320
Number of pages	6
ISBN (Electronic)	9783319152219
ISBN (Print)	9783319152202
DOIs	https://doi.org/10.1007/978-3-319-15221-9_28
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	United States
City	Orlando, FL
Period	2/02/15 → 5/02/15

Keywords

Nonlinearity
Differential evolution
Optimisation
Simplifying transformation
Superharmonics

Access to Document

10.1007/978-3-319-15221-9_28

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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_28. Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 283 KB

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Dervilis, N., Worden, K., Wagg, D. J., & Neild, S. A. (2015). Simplifying Transformations for Nonlinear Systems: Part I, An Optimisation-Based Variant of Normal Form Analysis. In G. Kerschen (Ed.), Nonlinear Dynamics, Volume 1: Proceedings of the 33rd IMAC, A Conference and Exposition on Structural Dynamics, 2015 (pp. 315-320). (Conference Proceedings of the Society for Experimental Mechanics Series). Springer. https://doi.org/10.1007/978-3-319-15221-9_28

Dervilis, N ; Worden, Keith ; Wagg, David J ; Neild, Simon A. / Simplifying Transformations for Nonlinear Systems : Part I, An Optimisation-Based Variant of Normal Form Analysis. Nonlinear Dynamics, Volume 1: Proceedings of the 33rd IMAC, A Conference and Exposition on Structural Dynamics, 2015. editor / Gaëtan Kerschen. Springer, 2015. pp. 315-320 (Conference Proceedings of the Society for Experimental Mechanics Series).

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title = "Simplifying Transformations for Nonlinear Systems: Part I, An Optimisation-Based Variant of Normal Form Analysis",

abstract = "This paper introduces the idea of a {\textquoteleft}simplifying transformation{\textquoteright} for nonlinear structural dynamic systems. The idea simply stated; is to bring under one heading, those transformations which {\textquoteleft}simplify{\textquoteright} structural dynamic systems or responses in some sense. The equations of motion may be cast in a simpler form or decoupled (and in this sense, nonlinear modal analysis is encompassed) or the responses may be modified in order to isolate and remove certain components. It is the latter sense of simplification which is considered in this paper. One can regard normal form analysis in a way as the removal of superharmonic content from nonlinear system response. In the current paper, this problem is cast in an optimisation form and the differential evolution algorithm is used.",

keywords = "Nonlinearity, Differential evolution, Optimisation, Simplifying transformation, Superharmonics",

author = "N Dervilis and Keith Worden and Wagg, {David J} and Neild, {Simon A}",

year = "2015",

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language = "English",

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

publisher = "Springer",

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Dervilis, N, Worden, K, Wagg, DJ & Neild, SA 2015, Simplifying Transformations for Nonlinear Systems: Part I, An Optimisation-Based Variant of Normal Form Analysis. 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. 315-320, 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_28

Simplifying Transformations for Nonlinear Systems : Part I, An Optimisation-Based Variant of Normal Form Analysis. / Dervilis, N; Worden, Keith; Wagg, David J; Neild, Simon A.

Nonlinear Dynamics, Volume 1: Proceedings of the 33rd IMAC, A Conference and Exposition on Structural Dynamics, 2015. ed. / Gaëtan Kerschen. Springer, 2015. p. 315-320 (Conference Proceedings of the Society for Experimental Mechanics Series).

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

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T1 - Simplifying Transformations for Nonlinear Systems

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PY - 2015/8/14

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N2 - This paper introduces the idea of a ‘simplifying transformation’ for nonlinear structural dynamic systems. The idea simply stated; is to bring under one heading, those transformations which ‘simplify’ structural dynamic systems or responses in some sense. The equations of motion may be cast in a simpler form or decoupled (and in this sense, nonlinear modal analysis is encompassed) or the responses may be modified in order to isolate and remove certain components. It is the latter sense of simplification which is considered in this paper. One can regard normal form analysis in a way as the removal of superharmonic content from nonlinear system response. In the current paper, this problem is cast in an optimisation form and the differential evolution algorithm is used.

AB - This paper introduces the idea of a ‘simplifying transformation’ for nonlinear structural dynamic systems. The idea simply stated; is to bring under one heading, those transformations which ‘simplify’ structural dynamic systems or responses in some sense. The equations of motion may be cast in a simpler form or decoupled (and in this sense, nonlinear modal analysis is encompassed) or the responses may be modified in order to isolate and remove certain components. It is the latter sense of simplification which is considered in this paper. One can regard normal form analysis in a way as the removal of superharmonic content from nonlinear system response. In the current paper, this problem is cast in an optimisation form and the differential evolution algorithm is used.

KW - Nonlinearity

KW - Differential evolution

KW - Optimisation

KW - Simplifying transformation

KW - Superharmonics

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M3 - Conference Contribution (Conference Proceeding)

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Y2 - 2 February 2015 through 5 February 2015

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Dervilis N, Worden K, Wagg DJ, Neild SA. Simplifying Transformations for Nonlinear Systems: Part I, An Optimisation-Based Variant of Normal Form Analysis. In Kerschen G, editor, Nonlinear Dynamics, Volume 1: Proceedings of the 33rd IMAC, A Conference and Exposition on Structural Dynamics, 2015. Springer. 2015. p. 315-320. (Conference Proceedings of the Society for Experimental Mechanics Series). https://doi.org/10.1007/978-3-319-15221-9_28

Simplifying Transformations for Nonlinear Systems: Part I, An Optimisation-Based Variant of Normal Form Analysis

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