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1/3 PURE SUB-HARMONIC SOLUTION AND FRACTAL CHARACTERISTIC OF TRANSIENT PROCESS FOR DUFFING'S EQUATION
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作者 徐玉秀 胡海岩 闻邦椿 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第9期1171-1176,共6页
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-har... 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. 展开更多
关键词 Duffing's equation SUB-HARMONIC transient process fractal characteristic sensitive dimension
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