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Backbone analysis for nonlinear vibrations in rotor dynamics

Alexander Shaw Orcid Logo, MEHMET AKAY, Michael Friswell

Nonlinear Dynamics, Volume: 114

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

  • Accepted Manuscript under embargo until: 25th April 2027

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
Published: 2026
URI: https://cronfa.swan.ac.uk/Record/cronfa71666
first_indexed 2026-03-24T16:15:20Z
last_indexed 2026-04-25T06:50:25Z
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spelling 2026-04-24T09:55:47.6253520 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 24 4 2026 2026-04-24 10.1007/s11071-026-12466-z COLLEGE NANME Aerospace Civil Electrical and Mechanical Engineering COLLEGE CODE ACEM Swansea University 2026-04-24T09:55:47.6253520 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 Under embargo Under embargo 2026-03-24T16:11:02.6184997 Output 3645600 application/pdf Accepted Manuscript true 2027-04-25T00:00:00.0000000 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
publishDate 2026
institution Swansea University
doi_str_mv 10.1007/s11071-026-12466-z
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace 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 2026-04-24T07:50:25Z
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