| 1/3 PURE SUB-HARMONIC SOLUTION AND FRACTAL CHARACTERISTIC OF TRANSIENT PROCESS FOR DUFFING＇S EQUATION |
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| 引用本文： | 徐玉秀,胡海岩,闻邦椿.1/3 PURE SUB-HARMONIC SOLUTION AND FRACTAL CHARACTERISTIC OF TRANSIENT PROCESS FOR DUFFING＇S EQUATION[J].应用数学和力学(英文版),2006,27(9):1171-1176. |
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| 作者姓名： | 徐玉秀 胡海岩 闻邦椿 |
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| 作者单位： | [1]School of Mechanical and Electronic Engineering,Tianjin Polytechnic University, Tianjin 300160, P. R. China [2]Institute of Vibrational Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China [3]School of Mechanical Engineering and Automation, Northeast University, Shenyang 110006, P. R. China |
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| 基金项目： | Project supported by the National Natural Science Foundation of China （No.50275024） |
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| 摘 要： | The 1/3 sub-harmonic solution for the Duffing＇s with damping equation was investigated by using the methods of harmonic balance and numerical integration. The assumed solution is introduced, and the domain of sub-harmonic frequencies was found. The asymptotical stability of the subharmonic resonances and the sensitivity of the amplitude responses to the variation of damping coefficient were examined. Then, the subharmonic resonances were analyzed by using the techniques from the general fractal theory. The analysis indicates that the sensitive dimensions of the system time-field responses show sensitivity to the conditions of changed initial perturbation, changed damping coefficient or the amplitude of excitation, thus the sensitive dimension can clearly describe the characteristic of the transient process of the subharmonic resonances.
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| 关 键 词： | Duffing方程 次谐波 瞬时进程 分形特征 |
| 文章编号： | 10.1007/s10483-006-0903-1 |
| 收稿时间： | 2005-04-05 |
| 修稿时间： | 2006-04-13 |
1/3 Pure sub-harmonic solution and fractal characteristic of transient process for Duffing’s equation |
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| Yu-xiu Xu Doctor,Hai-yan Hu,Bang-chun Wen.1/3 Pure sub-harmonic solution and fractal characteristic of transient process for Duffing’s equation[J].Applied Mathematics and Mechanics(English Edition),2006,27(9):1171-1176. |
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| Authors: | Yu-xiu Xu Doctor Hai-yan Hu Bang-chun Wen |
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| Institution: | (1) School of Mechanical and Electronic Engineering, Tianjin Polytechnic University, Tianjin, 300160, P. R. China;(2) Institute of Vibrational Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, P. R. China;(3) School of Mechanical Engineering and Automation, Northeast University, Shenyang, 110006, P. R. China |
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| Abstract: | The 1/3 sub-harmonic solution for the Duffing’s with damping equation was investigated by using the methods of harmonic balance
and numerical integration. The assumed solution is introduced, and the domain of sub-harmonic frequencies was found. The asymptotical
stability of the subharmonic resonances and the sensitivity of the amplitude responses to the variation of damping coefficient
were examined. Then, the subharmonic resonances were analyzed by using the techniques from the general fractal theory. The
analysis indicates that the sensitive dimensions of the system time-field responses show sensitivity to the conditions of
changed initial perturbation, changed damping coefficient or the amplitude of excitation, thus the sensitive dimension can
clearly describe the characteristic of the transient process of the subharmonic resonances.
Project supported by the National Natural Science Foundation of China (No.50275024) |
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| Keywords: | Duffing’ s equation sub-harmonic transient process fractal characteristic sensitive dimension |
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