Backbone analysis for nonlinear vibrations in rotor dynamics

Shaw, Alexander; AKAY, MEHMET; Friswell, Michael

doi:10.1007/s11071-026-12466-z

Journal article 246 views 9 downloads

Backbone analysis for nonlinear vibrations in rotor dynamics

Alexander Shaw

, MEHMET AKAY, Michael Friswell

Nonlinear Dynamics, Volume: 114, Issue: 8, Start page: 611

Swansea University Authors: Alexander Shaw , MEHMET AKAY, Michael Friswell

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DOI (Published version): 10.1007/s11071-026-12466-z

Abstract

Backbone curves are a well established practice for understanding the vibrations of nonlinear structures, by charting the frequency-amplitude relations for the underlying conservative system. However, in their typical form they are ineffective in tracing many of the phenomena seen in the lateral vib...

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Published in:	Nonlinear Dynamics
ISSN:	0924-090X 1573-269X
Published:	Springer Nature 2026
Online Access:	Check full text
URI:	https://cronfa.swan.ac.uk/Record/cronfa71666

first_indexed	2026-03-24T16:15:20Z
last_indexed	2026-06-09T08:54:12Z
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However, in their typical form they are ineffective in tracing many of the phenomena seen in the lateral vibrations of an isotropically supported rotating disk, which include both periodic, quasiperiodic and isolated responses. This is because the underlying conservative system lacks mechanisms to drive the mode locking that is an essential part of these responses. However, to include effects such as unbalance forcing that can induce these behaviours would reduce the generality of the analysis, and may also require knowledge of parameters that can be difficult to control or measure. This work produces backbone curves with additional constraints to ensure that the response remains in phase with the unbalance forcing, acting in the place of the physical causes of mode locking. These curves provide a skeleton that sits underneath the bifurcation diagrams of a wide range of nonconservative and also weakly anisotropic rotating disc systems, despite being calculated with just the underlying conservative and isotropic parts of the system. This allows a systematic means of exploring the complex response space of rotating systems, enabling continuation approaches to efficiently find isolated response regions that previously required a sweep of many time simulations to discover. The approach provides some commonality to the analysis of a diverse range of responses. The method is demonstrated on an isotropic 2 degree of freedom overhung rotor with a smooth radial stiffness nonlinearity, but is shown to have relevance to nonsmooth systems and weakly anisotropic systems. 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spelling	2026-06-08T11:07:00.0168179 v2 71666 2026-03-24 Backbone analysis for nonlinear vibrations in rotor dynamics 10cb5f545bc146fba9a542a1d85f2dea 0000-0002-7521-827X Alexander Shaw Alexander Shaw true false b1366490e021f33010551e3d84333829 MEHMET AKAY MEHMET AKAY true false 5894777b8f9c6e64bde3568d68078d40 Michael Friswell Michael Friswell true false 2026-03-24 ACEM Backbone curves are a well established practice for understanding the vibrations of nonlinear structures, by charting the frequency-amplitude relations for the underlying conservative system. However, in their typical form they are ineffective in tracing many of the phenomena seen in the lateral vibrations of an isotropically supported rotating disk, which include both periodic, quasiperiodic and isolated responses. This is because the underlying conservative system lacks mechanisms to drive the mode locking that is an essential part of these responses. However, to include effects such as unbalance forcing that can induce these behaviours would reduce the generality of the analysis, and may also require knowledge of parameters that can be difficult to control or measure. This work produces backbone curves with additional constraints to ensure that the response remains in phase with the unbalance forcing, acting in the place of the physical causes of mode locking. These curves provide a skeleton that sits underneath the bifurcation diagrams of a wide range of nonconservative and also weakly anisotropic rotating disc systems, despite being calculated with just the underlying conservative and isotropic parts of the system. This allows a systematic means of exploring the complex response space of rotating systems, enabling continuation approaches to efficiently find isolated response regions that previously required a sweep of many time simulations to discover. The approach provides some commonality to the analysis of a diverse range of responses. The method is demonstrated on an isotropic 2 degree of freedom overhung rotor with a smooth radial stiffness nonlinearity, but is shown to have relevance to nonsmooth systems and weakly anisotropic systems. An experimental comparison is also given. Journal Article Nonlinear Dynamics 114 8 611 Springer Nature 0924-090X 1573-269X Rotordynamics; Backbone curves; Modal interaction; Internal resonance; Numerical continuation 30 4 2026 2026-04-30 10.1007/s11071-026-12466-z COLLEGE NANME Aerospace Civil Electrical and Mechanical Engineering COLLEGE CODE ACEM Swansea University Not Required 2026-06-08T11:07:00.0168179 2026-03-24T16:08:34.0852210 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering Alexander Shaw 0000-0002-7521-827X 1 MEHMET AKAY 2 Michael Friswell 3 71666__36452__9766cc53ee7f416d90e7b24e37a510c9.pdf rbb_revision2_clean.pdf 2026-03-24T16:11:02.6184997 Output 3645600 application/pdf Accepted Manuscript true Author accepted manuscript document released under the terms of a Creative Commons CC-BY licence using the Swansea University Research Publications Policy (rights retention). true eng https://creativecommons.org/licenses/by/4.0/deed.en
title	Backbone analysis for nonlinear vibrations in rotor dynamics
spellingShingle	Backbone analysis for nonlinear vibrations in rotor dynamics Alexander Shaw MEHMET AKAY Michael Friswell
title_short	Backbone analysis for nonlinear vibrations in rotor dynamics
title_full	Backbone analysis for nonlinear vibrations in rotor dynamics
title_fullStr	Backbone analysis for nonlinear vibrations in rotor dynamics
title_full_unstemmed	Backbone analysis for nonlinear vibrations in rotor dynamics
title_sort	Backbone analysis for nonlinear vibrations in rotor dynamics
author_id_str_mv	10cb5f545bc146fba9a542a1d85f2dea b1366490e021f33010551e3d84333829 5894777b8f9c6e64bde3568d68078d40
author_id_fullname_str_mv	10cb5f545bc146fba9a542a1d85f2dea_*_Alexander Shaw b1366490e021f33010551e3d84333829__MEHMET AKAY 5894777b8f9c6e64bde3568d68078d40_**_Michael Friswell
author	Alexander Shaw MEHMET AKAY Michael Friswell
author2	Alexander Shaw MEHMET AKAY Michael Friswell
format	Journal article
container_title	Nonlinear Dynamics
container_volume	114
container_issue	8
container_start_page	611
publishDate	2026
institution	Swansea University
issn	0924-090X 1573-269X
doi_str_mv	10.1007/s11071-026-12466-z
publisher	Springer Nature
college_str	Faculty of Science and Engineering
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description	Backbone curves are a well established practice for understanding the vibrations of nonlinear structures, by charting the frequency-amplitude relations for the underlying conservative system. However, in their typical form they are ineffective in tracing many of the phenomena seen in the lateral vibrations of an isotropically supported rotating disk, which include both periodic, quasiperiodic and isolated responses. This is because the underlying conservative system lacks mechanisms to drive the mode locking that is an essential part of these responses. However, to include effects such as unbalance forcing that can induce these behaviours would reduce the generality of the analysis, and may also require knowledge of parameters that can be difficult to control or measure. This work produces backbone curves with additional constraints to ensure that the response remains in phase with the unbalance forcing, acting in the place of the physical causes of mode locking. These curves provide a skeleton that sits underneath the bifurcation diagrams of a wide range of nonconservative and also weakly anisotropic rotating disc systems, despite being calculated with just the underlying conservative and isotropic parts of the system. This allows a systematic means of exploring the complex response space of rotating systems, enabling continuation approaches to efficiently find isolated response regions that previously required a sweep of many time simulations to discover. The approach provides some commonality to the analysis of a diverse range of responses. The method is demonstrated on an isotropic 2 degree of freedom overhung rotor with a smooth radial stiffness nonlinearity, but is shown to have relevance to nonsmooth systems and weakly anisotropic systems. An experimental comparison is also given.
published_date	2026-04-30T06:01:39Z
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score	11.109323

Backbone analysis for nonlinear vibrations in rotor dynamics

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