On some aspects of the dynamic behavior of the softening Duffing oscillator under harmonic excitation
On some aspects of the dynamic behavior of the softening Duffing oscillator under harmonic excitation
复制标题
谐波激励下软化杜芬振子动态行为的若干问题
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
L. Lentz
中科院分区：
文献类型：
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作者：
U. Wagner;L. Lentz
Duffing振子可能是动力学中最常见的非线性振子。考虑到弱阻尼和简谐激励的软化Duffing振子的情况，并执行标准的方法，如谐波平衡或摄动分析，零均值解与大振幅的小激励频率。这些解在幅频图中产生“鼻状”曲线，并与倾斜的共振曲线合并，以减小（但不为零）阻尼。这些结果在几本教科书中没有任何额外的讨论。本文通过引入谐波平衡法中的误差估计，讨论了这些解的精度。执行修改后的扰动分析，导致解决方案与非零的平均值，显示非常小的误差，在谐波平衡误差分析。
The Duffing oscillator is probably the most popular example of a nonlinear oscillator in dynamics. Considering the case of softening Duffing oscillator with weak damping and harmonic excitation and performing standard methods like harmonic balance or perturbation analysis, zero mean solutions with large amplitudes are found for small excitation frequencies. These solutions produce a ”nose-like” curve in the amplitude–frequency diagram and merge with the inclining resonance curve for decreasing (but non-vanishing) damping. These results are presented without any additional discussion in several textbooks. The present paper discusses the accurateness of these solutions by introducing an error estimation in the harmonic balance method showing large errors. Performing a modified perturbation analysis leads to solutions with non-vanishing mean value, showing very small errors in the harmonic balance error analysis.