Open AccessBifurcation and chaos of some strongly nonlinear relative rotation system with time-varying clearance
Author(s) -
Bin Liu,
Zhao Hong-xu,
Hou Dong-Xiao,
Haoran Liu
Publication year - 2014
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.63.074501
Subject(s) - bifurcation , period doubling bifurcation , nonlinear system , physics , saddle node bifurcation , bifurcation diagram , bifurcation theory , mathematical analysis , motion (physics) , mathematics , classical mechanics , control theory (sociology) , computer science , quantum mechanics , control (management) , artificial intelligence
The dynamic equation for the relative rotation nonlinear dynamic system with time-varying clearance is investigated. Firstly, transformation parameter is deduced by using the method of MLP; the bifurcation response equations of 1/2 harmonic resonance then are generated by the method of multiple scales, while singularity analysis is employed to obtain the transition set of steady motion; further more the bifurcation characteristic and the bifurcation of the system under the situation of non-autonomy are analyzed. Finally, numerical simulation exhibits many different motions, such as periodic motion, period-doubling motion, and chaos. It is shown that the change of clearance and damp parameters may influence the motion state of the system.