Piecewise Analytical Solution for Rub Interactions Between a Rotor and an Asymmetrically Supported Stator

Heba El-Mongy, Tamer El-Sayed* (Corresponding Author), Vahid Vaziri, Marian Wiercigroch

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingPublished conference contribution


Rotor-stator rubbing phenomenon is a very common fault in various engineering applications. Usually, the stator supports are assumed to be symmetric, however, in some conditions, the stator support stiffness is anisotropic in nature. In this paper, an approximate analytical solution for the rub interactions between a Jeffcott rotor and an asymmetrically supported stator is introduced. The present problem is a good example of piecewise nonlinear dynamics in which contact causes the system to switch between linear and nonlinear dynamic behavior. To evaluate an analytical solution to the contact equations, Taylor’s expansion is used to linearize the contact forces. Then, an analytical solution is introduced based on this approximation. To investigate the validity of the present model, the proposed approximate analytical solution is compared with the numerical solution obtained using direct numerical integration for the same problem. The results show that the proposed piecewise analytical solution is efficient in evaluating the system response for both periodic and chaotic responses.
Original languageEnglish
Title of host publicationRecent Trends in Wave Mechanics and Vibrations. WMVC 2022. Mechanisms and Machine Science
EditorsZ. Dimitrovová, P. Biswas, R. Gonçalves, T. Silva
Number of pages8
ISBN (Electronic)978-3-031-15758-5
ISBN (Print)978-3-031-15757-8
Publication statusPublished - 7 Oct 2022
EventWMVC 2022: 10th International Conference on Wave Mechanics and Vibrations - Lisbon, Portugal
Duration: 4 Jul 20226 Jul 2022
Conference number: 10th

Publication series

NameMechanisms and Machine Science
ISSN (Print)2211-0984
ISSN (Electronic)2211-0992


ConferenceWMVC 2022
Abbreviated titleWMVC 2022
Internet address


  • Rotordynamics
  • Asymmetric stator
  • Jeffcott rotor
  • Analytical solution
  • Periodic
  • Piecewise nonlinear system


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