Normal form analysis of bouncing cycles in isotropic rotor stator contact problems

Alexander D Shaw*, Alan R. Champneys, Michael I. Friswell

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

16 Citations (Scopus)
81 Downloads (Pure)


This work considers analysis of sustained bouncing responses of rotating shafts with nonlinear lateral vibrations due to rotor stator contact. The insight that this is an internal resonance phenomena makes this an ideal system to be studied with the method of normal forms, which assumes that a system may be modelled primarily in terms of just its resonant response components. However, the presence of large non smooth nonlinearities due to impact and rub mean that the method must be extended. This is achieved here by incorporating an alternating frequency/time (AFT) step to capture nonlinear forces. Furthermore, the presence of gyroscopic terms leads to the need to handle complex modal variables, and a rotating coordinate frame must be used to obtain periodic responses. The process results in an elegant formulation that can provide reduced order models of a wide variety of rotor systems, with potentially many nonlinear degrees of freedom. The method is demonstrated by comparing against time simulation of two example rotors, demonstrating high precision on a simple model and approximate precision on a larger model.

Original languageEnglish
Pages (from-to)83-97
Number of pages15
JournalInternational Journal of Mechanical Sciences
Early online date25 Feb 2019
Publication statusPublished - 1 May 2019

Structured keywords

  • Engineering Mathematics Research Group


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