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| Periodic solution and its approximate analytic expressions of the nonlinear rotor-bearing system |
| Revised:December 20, 2002 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20045099 |
| KeyWord:nonlinear,shooting method,periodic solution,rotor-bearing system,the harmonic balance method |
| Li Dexin~* Xu Jianxue |
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| Abstract: |
| In this paper, a generalized shooting method and a harmonic balancing method to determine the periodic orbit, its period and the approximate analytic expression of the nonlinear bearing-rotor system are presented. At first, by changing the time scale, the period of the periodic orbit of the nonlinear system is drawn into the governing equation of the system explicitly. Then, the generalized shooting procedure is recompiled; the period takes part into the iteration procedure of the shooting method as a parameter. The iteration procedure includes the solving of the periodic orbit and its period. The increment value changed in the iteration procedure is selected by using the optimization method, and then the periodic orbit and its period of the system are determined rapidly. The approximate analytic expression of the nonlinear bearing-rotor system is obtained by using the results solved combined with the harmonic method. The periodic solutions of any precision can be obtained by adding the number of the order of the harmonics theoretically. At last, applying this method into the nonlinear rotor-bearing system, the periodic solution and its approximate analytic expression of the nonlinear bearing-rotor system are obtained under the condition of some parameters. The validity of the method has been verified by comparing with the results of the 4-order Runge-Kutta numerical integral method. The results make important theoretic sense in the controlling of the motion of the rotor-bearing system. |
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