Backbone analysis for nonlinear vibrations in rotor dynamics

Backbone analysis for nonlinear vibrations in rotor dynamics | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Backbone analysis for nonlinear vibrations in rotor dynamics Alexander David Shaw, Mehmet Salim Akay, Michael Ian Friswell This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8262746/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 24 Apr, 2026 Read the published version in Nonlinear Dynamics → Version 1 posted 4 You are reading this latest preprint version Abstract Backbone curves, a form of nonlinear normal mode analysis, 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 vibrations of isotropic rotating systems, including both periodic responses related to the main resonance and isolated quasiperiodic responses. This is because in the fully conservative and isotropic system there are no mechanisms to drive the mode locking that is an essential part of these responses. However, to include mechanisms such as out of balance forcing that can induce these behaviours would reduce the generality of the analysis, and may also require knowledge of parameters that can be hard to control or measure. This work produces backbones curves with additional constraints that enforce synchronisation with the out of balance forcing and therefore act 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 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 more efficiently find isolated response regions that previously required brute force simulation approaches to discover. The approach also 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 harsher nonlinearity systems and weakly anisotropic systems. An experimental comparison is also given. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 24 Apr, 2026 Read the published version in Nonlinear Dynamics → Version 1 posted Editorial decision: Revision requested 08 Dec, 2025 Editor assigned by journal 08 Dec, 2025 Submission checks completed at journal 08 Dec, 2025 First submitted to journal 02 Dec, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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