| Neimark-Sacker （N-S） in bifurcation of oscillator with dry friction 1：4 strong resonance |
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| 引用本文： | 郭勇,谢建华. Neimark-Sacker （N-S） in bifurcation of oscillator with dry friction 1：4 strong resonance[J]. 应用数学和力学(英文版), 2013, 34(1): 27-36. DOI: 10.1007/s10483-013-1650-9 |
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| 作者姓名： | 郭勇 谢建华 |
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| 作者单位： | School of Mechanics and Engineering,Southwest Jiaotong University |
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| 基金项目： | Project supported by the National Natural Science Foundation of China(No.11172246);the Fundamental Research Funds for the Central Universities of China(No.SWJTU11ZT15) |
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| 摘 要： | An oscillator with dry friction under external excitation is considered.The Poincaré map can be established according to the series solution near equilibrium in the case of 1:4 resonance.Based on the theory of normal forms,the map is reduced into its normal form.It is shown that the Neimark-Sacker(N-S) bifurcations may occour.The theoretical results are verified with the numerical simulations.
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| 关 键 词： | dry friction Poincaré map normal form periodic solution torus |
| 收稿时间： | 2012-03-30 |
Neimark-Sacker (N-S) bifurcation of oscillator with dry friction in 1:4 strong resonance |
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| Yong Guo,Jian-hua Xie. Neimark-Sacker (N-S) bifurcation of oscillator with dry friction in 1:4 strong resonance[J]. Applied Mathematics and Mechanics(English Edition), 2013, 34(1): 27-36. DOI: 10.1007/s10483-013-1650-9 |
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| Authors: | Yong Guo Jian-hua Xie |
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| Affiliation: | School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, P. R. China |
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| Abstract: | An oscillator with dry friction under external excitation is considered. The Poincaré map can be established according to the series solution near equilibrium in the case of 1:4 resonance. Based on the theory of normal forms, the map is reduced into its normal form. It is shown that the Neimark-Sacker (N-S) bifurcations may occour. The theoretical results are verified with the numerical simulations. |
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| Keywords: | dry friction Poincar´e map normal form periodic solution torus |
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