Principal resonance responses of SDOF systems with small fractional derivative damping under narrow-band random parametric excitation
Principal resonance responses of SDOF systems with small fractional derivative damping under narrow-band random parametric excitation
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窄带随机参数激励下小分数阶导数阻尼单自由度系统的主共振响应
DOI：
10.1016/j.cnsns.2014.03.018
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发表时间：
2014-10
影响因子：
3.9
通讯作者：
Xu Yong
中科院分区：
文献类型：
--
作者：
Liu Di;Li Jing;Xu Yong
研究了α（0 <α< 1）阶分数阶微阻尼非线性单自由度系统在窄带随机参数激励下的主共振响应。利用多尺度法导出了振幅和相位的两个一阶随机微分方程，研究了分数阶和随机激励强度对一阶和二阶矩的影响。作为例子，考虑了具有分数阶导数阻尼的随机Duffing振子。利用最大李雅普诺夫指数研究了失谐频率参数、随机激励强度和分数阶导数阻尼对系统稳定性的影响。相应的理论结果通过直接数值模拟得到了很好的验证。另外，利用有限差分法分析了参数主共振响应的随机跳跃现象。随机跳跃现象表明，当激励强度很小时，振幅响应的最可几运动在较大的非平凡分支附近，随着激励强度的增加，振幅响应的可几运动将从较大的非平凡分支向平凡分支移动。这种随机跳跃可以被认为是分岔。
The principal resonance responses of nonlinear single-degree-of-freedom (SDOF) systems with lightly fractional derivative damping of orderα(0 <α< 1) subject to the narrow-band random parametric excitation are investigated. The method of multiple scales is developed to derive two first order stochastic differential equation of amplitude and phase, and then to examine the influences of fractional order and intensity of random excitation on the first-order and second-order moment. As an example, the stochastic Duffing oscillator with fractional derivative damping is considered. The effects of detuning frequency parameter, the intensity of random excitation and the fractional order derivative damping on stability are studied through the largest Lyapunov exponent. The corresponding theoretical results are well verified through direct numerical simulations. In addition, the phenomenon of stochastic jump is analyzed for parametric principal resonance responses via finite differential method. The stochastic jump phenomena indicates that the most probable motion is around the larger non-trivial branch of the amplitude response when the intensity of excitation is very small, and the probable motion of amplitude responses will move from the larger non-trivial branch to trivial branch with the increasing of the intensity of excitation. Such stochastic jump can be considered as bifurcation.
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DOI：
10.1016/j.ijnonlinmec.2005.08.002
发表时间：
2006-03
影响因子：
3.2
作者：
Y. Rossikhin;M. Shitikova
通讯作者：
Y. Rossikhin;M. Shitikova
影响因子：
5.6
作者：
O. Agrawal
通讯作者：
O. Agrawal
影响因子：
4.7
作者：
O. Agrawal
通讯作者：
O. Agrawal
DOI：
10.1080/14786443808562036
发表时间：
1938-03
期刊：
Philosophical Magazine Series 1
影响因子：
--
作者：
A. Gemant
通讯作者：
A. Gemant
影响因子：
4.5
作者：
C. Koh;J. Kelly
通讯作者：
C. Koh;J. Kelly