Semi-analytical predictions of multi-stable independent periodic motions and bifurcation evolution in a nonlinear bolted rotor system. (English) Zbl 1540.70035
Summary: The bolted structures have the advantages of high specific strength and easy maintenance, which are widely used in rotating machines such as gas turbines and aero-engines. Meanwhile, the complex nonlinear motions and bifurcations are easily induced by the nonlinear stiffness caused by the bolted structure in rotor systems, but these characteristics cannot be fully revealed only by numerical results. In this research, an analytical model of a bolted rotor system considering contact nonlinearity is established. The global bifurcation trees and semi-analytical periodic motions of the system are presented by the implicit discrete mapping method, which are also compared to the numerical solutions for validation. Multi-stable phenomena of independent periodic motions P-3\((m+1)\), \((m=0,1,2)\) are discovered, the bifurcation jumping phenomena between the higher-order and lower-order motions are revealed, the occurrence of unstable motions is indicated in Neimark bifurcation judged by eigenvalues. In addition, the independence of the higher-order periodic motions in bifurcation tree is proved. Finally, the periodic motions of the nonlinear rotor system are numerically predicted by harmonic amplitudes and phase characteristics. These findings provide clear and complete solutions for understanding and presenting the nonlinear dynamic characteristics of bolted rotor systems considering the contact effect, which have great potential in guiding the dynamic design and parameter adjustment of practical rotating machines.
MSC:
| 70K50 | Bifurcations and instability for nonlinear problems in mechanics |
| 70K42 | Equilibria and periodic trajectories for nonlinear problems in mechanics |
Keywords:
contact nonlinearity; global bifurcation tree; implicit discrete mapping method; bifurcation jumping; Neimark bifurcationReferences:
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