| 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) |
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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： | School of Mechanical and Electronic Engineering Tianjin Polytechnic University Tianjin 300160 P. R. China，Institute of Vibrational Engineering Nanjing University of Aeronautics and Astronautics Nanjing 210016 P. R. China，School of Mechanical Engineering and Automation Northeast University Shenyang 110006 P. R. China |
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| 摘 要： | The 1/3 sub-harmonic solution for the Buffing'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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1/3 PURE SUB-HARMONIC SOLUTION AND FRACTAL CHARACTERISTIC OF TRANSIENT PROCESS FOR DUFFING''''S EQUATION |
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| XU Yu-xiu,HU Hai-yan,WEN Bang-chun. 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) |
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| Authors: | XU Yu-xiu HU Hai-yan WEN Bang-chun |
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| Abstract: | The 1/3 sub-harmonic solution for the Buffing'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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| Keywords: | Buffing's equation sub-harmonic transient process fractal characteristic sensitive dimension |
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