| 强迫振动下Duffing方程的摄动解分析 |
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| 引用本文： | 张艳丹,江新华. 强迫振动下Duffing方程的摄动解分析[J]. 北京化工大学学报(自然科学版), 2016, 43(3): 126. DOI: 10.13543/j.bhxbzr.2016.03.021 |
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| 作者姓名： | 张艳丹 江新华 |
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| 作者单位： | 北京化工大学理学院,北京,100029;北京化工大学理学院,北京,100029 |
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| 基金项目： | 国家自然科学基金(11171340) |
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| 摘 要： | 讨论了强迫振动下的非线性 Duffing 方程的摄动问题。 运用多重尺度法构造出渐近近似解,最后通过Gronwall 不等式对余项进行估计,证明了近似解的一致有效性。
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| 关 键 词： | Duffing方程 多重尺度法 强迫振动 误差分析 |
| 收稿时间： | 2016-01-11 |
Perturbation analysis for a Duffing equation with forced oscillations |
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| ZHANG YanDan,IANG XinHua. Perturbation analysis for a Duffing equation with forced oscillations[J]. Journal of Beijing University of Chemical Technology, 2016, 43(3): 126. DOI: 10.13543/j.bhxbzr.2016.03.021 |
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| Authors: | ZHANG YanDan IANG XinHua |
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| Affiliation: | Faculty of Science, Beijing University of Chemical Technology, Beijing 100029, China |
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| Abstract: | Duffing equations have very significant value in mechanical oscillators systems. In this paper, nonlinear Duffing equation with forced oscillations is considered and the perturbation technique is applied. The multiple scales method is utilized to obtain the asymptotic approximation solution. The Gronwall inequality is also applied to estimate the error and the uniform validity of the perturbed solution is proved. |
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| Keywords: | Duffing equation the multiple scales method forced oscillation error analysis |
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