Bistability and stochastic jumps in an airfoil system with viscoelastic material property and random fluctuations
Bistability and stochastic jumps in an airfoil system with viscoelastic material property and random fluctuations
复制标题
具有粘弹性材料特性和随机波动的翼型系统中的双稳定性和随机跳跃
DOI：
10.1016/j.cnsns.2020.105184
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发表时间：
2020-05
影响因子：
3.9
通讯作者：
Kurths Juergen
中科院分区：
文献类型：
--
作者：
Liu Qi;Xu Yong;Kurths Juergen
本文的目的是解析地探讨随机波动对带有粘弹性项的两自由度翼型模型的影响。首先，利用指数衰减核函数上的卷积积分来建立粘弹性材料的本构关系。然后介绍了相应的具有粘弹性项和随机激励的TDOF翼型模型。随后，通过多尺度方法和摄动技术对所提出的翼型模型进行了理论分析。所有得到的近似解析解都得到了数值模拟结果的验证，并得到了较好的一致性。同时，我们还发现在一定的激励频率或幅度范围内，高振幅和低振幅的振荡同时存在，这被认为是一种双稳态行为。此外，还详细研究了粘弹性项和随机激励对系统响应的影响。我们发现粘弹性项对系统动力学有相当大的影响，可以同时影响翼型系统的结构阻尼和刚度。更有趣的是，由于随机波动可以引起高振幅和低振幅振荡之间的随机跳跃，这通过时间历史和稳态概率密度函数得到进一步说明。跳跃被认为是从一种可能状态到另一种状态的转变，反之亦然。这些结果表明，外部随机波动对具有粘弹性材料特性的TDOF翼型模型的动力学特性有显著的影响。
The purpose of this paper is to explore analytically the influences of random fluctuations on a two-degrees-of-freedom (TDOF) airfoil model with viscoelastic terms. To begin with, a convolution integral over an exponentially decaying kernel function is employed to establish a constitutive relation of the viscoelastic material. Then the corresponding TDOF airfoil model with viscoelastic terms and random excitations is introduced. Subsequently, a theoretical analysis for the proposed airfoil model is achieved through a multiple-scale method together with a perturbation technique. All of the obtained approximate analytical solutions are verified by numerical simulation results, and a good agreement is observed. Meanwhile, we also find that both high-amplitude and low-amplitude oscillations coexist within a certain range of the excitation frequency or amplitude, which is regarded as a bi-stable behavior. In addition, effects of the viscoelastic terms and the random excitations on the system responses are investigated in detail. We uncover that the viscoelastic terms have a considerable influence on the system dynamics, which can simultaneously affect the structural damping and stiffness of the airfoil system. More interestingly, stochastic jumps between high-amplitude and low-amplitude oscillations can be induced due to random fluctuations, which are further illustrated through time history and steady-state probability density function. The jumps are considered as a transition from one probable state to another or vice versa. These results indicate that the external random fluctuations have a remarkable influence on dynamics of the TDOF airfoil model with viscoelastic material property.
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DOI：
10.1115/smasis2012-7908
发表时间：
2012-09
期刊：
--
影响因子：
--
作者：
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通讯作者：
A. Bibo;M. Daqaq
影响因子：
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作者：
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DOI：
10.1137/090754819
发表时间：
2010-01
期刊：
SIAM J. Appl. Math.
影响因子：
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作者：
O. Gendelman;A. Vakakis;L. Bergman;D. McFarland
通讯作者：
O. Gendelman;A. Vakakis;L. Bergman;D. McFarland
DOI：
10.1016/j.cnsns.2013.09.022
发表时间：
2014-05
期刊：
Commun. Nonlinear Sci. Numer. Simul.
影响因子：
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作者：
R. Vasconcellos;A. Abdelkefi;M. Hajj;F. Marques
通讯作者：
R. Vasconcellos;A. Abdelkefi;M. Hajj;F. Marques