Stochastic bifurcations in the nonlinear vibroimpact system with fractional derivative under random excitation
Stochastic bifurcations in the nonlinear vibroimpact system with fractional derivative under random excitation
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随机激励下分数阶非线性振动冲击系统的随机分岔
DOI：
10.1016/j.cnsns.2016.05.004
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发表时间：
2017
影响因子：
3.9
通讯作者：
Xiao Yanwen
中科院分区：
文献类型：
--
作者：
Yang Yongge;Xu Wei;Sun Yahui;Xiao Yanwen
研究了具有分数阶导数的非线性碰撞振动系统在随机激励下的随机分岔。首先将原分数阶导数随机碰撞振动系统转化为不含分数阶导数的等价随机碰撞振动系统。然后，利用非光滑变换和随机平均法得到了等效随机系统的解析解。最后，为了验证上述方法的有效性，对具有分数阶导数的货车der Pol碰撞振动系统进行了详细的计算。分析结果与数值计算结果吻合得很好。本文发现了一个有趣的现象，即随机货车der Pol碰撞振动系统的分数阶和分数阶系数可以导致随机P-分岔的发生。据作者所知，在目前研究高斯白色噪声激励下分数阶导数随机系统动力学行为的文献中，还没有发现分数阶和分数阶系数诱导的随机P-分岔现象。
This paper aims to investigate the stochastic bifurcations in the nonlinear vibroimpact system with fractional derivative under random excitation. Firstly, the original stochastic vibroimpact system with fractional derivative is transformed into equivalent stochastic vibroimpact system without fractional derivative. Then, the non-smooth transformation and stochastic averaging method are used to obtain the analytical solutions of the equivalent stochastic system. At last, in order to verify the effectiveness of the above mentioned approach, the van der Pol vibroimpact system with fractional derivative is worked out in detail. A very satisfactory agreement can be found between the analytical results and the numerical results. An interesting phenomenon we found in this paper is that the fractional order and fractional coefficient of the stochastic van der Pol vibroimpact system can induce the occurrence of stochastic P-bifurcation. To the best of authors’ knowledge, the stochastic P-bifurcation phenomena induced by fractional order and fractional coefficient have not been found in the present available literature which studies the dynamical behaviors of stochastic system with fractional derivative under Gaussian white noise excitation.
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作者：
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作者：
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