, Volume 5, Issue 3, pp 257283
Modelocking in nonlinear rotordynamics
 G. H. M. van der HeijdenAffiliated withMathematics Institute, University of Utrecht
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We present a computerassisted study of the dynamics of two nonlinearly coupled driven oscillators with rotational symmetry which arise in rotordynamics (the nonlinearity coming from bearing clearance). The nonlinearity causes a splitting of the twofold degenerate natural frequency of the associated linear model, leading to three interacting frequencies in the system. Partial modelocking then yields a biinfinite series of attracting invariant 2tori carrying (quasi) periodic motion.
Due to the resonance nature, the (quasi) periodic solutions become periodic in a corotating coordinate system. They can be viewed as entrainments of periodic solutions of the associated linear problem. One presumably infinite family is generated by (scaled) driving frequencies ω = 1+2/n,n = 1,2,3,...; another one is generated by frequencies ω =m,m = 4,5,6,... Both integersn andm can be related to discrete symmetry properties of the particular periodic solutions.
Under a perturbation that breaks the rotational symmetry, more complicated behavior is possible. In particular, a second rational relation between the frequencies can be established, resulting in fully modelocked periodic motion.
Key words
rotor dynamics bearing clearance modelocking resonance Title
 Modelocking in nonlinear rotordynamics
 Journal

Journal of Nonlinear Science
Volume 5, Issue 3 , pp 257283
 Cover Date
 199505
 DOI
 10.1007/BF01212957
 Print ISSN
 09388974
 Online ISSN
 14321467
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 rotor dynamics
 bearing clearance
 modelocking
 resonance
 Authors

 G. H. M. van der Heijden ^{(1)}
 Author Affiliations

 1. Mathematics Institute, University of Utrecht, Utrecht, The Netherlands