Dynamic responses of axially moving viscoelastic beam under a randomly disordered periodic excitation
Dynamic responses of axially moving viscoelastic beam under a randomly disordered periodic excitation
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随机无序周期性激励下轴向移动粘弹性梁的动态响应
DOI：
10.1016/j.jsv.2012.04.005
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发表时间：
2012-08
影响因子：
4.7
通讯作者：
Xu, Yong
中科院分区：
文献类型：
--
作者：
Liu, Di;Xu, Wei;Xu, Yong
研究了轴向运动粘弹性梁在随机无序周期激励下的动力响应。用多尺度法推导了解的一阶一致展开式的解析表达式。基于最大Lyapunov指数，研究了平凡定态解的几乎必然稳定性。同时，我们得到了非平凡定态解的一阶和二阶定态矩。特别地，我们从理论和数值上对第一模进行了讨论。结果表明，在参数相同的情况下，随着随机激励强度的增大，非平凡稳态解的涨落将变得剧烈，从而导致非平凡稳态解失稳，平凡稳态解成为可能。在参数主共振的情况下，观察到第一阶振型的随机跳跃，这表明当随机激励较小时，平稳联合概率密度集中在非平凡解分支，但随着随机激励强度的增大，平凡稳态解的概率变大。这种随机跳跃现象可以定义为随机分叉。
We investigate dynamic responses of axially moving viscoelastic beam subject to a randomly disordered periodic excitation. The method of multiple scales is used to derive the analytical expression of first-order uniform expansion of the solution. Based on the largest Lyapunov exponent, the almost sure stability of the trivial steady-state solution is examined. Meanwhile, we obtain the first-order and the second-order steady-state moments for the non-trivial steady-state solutions. Specially, we discuss the first mode theoretically and numerically. Results show that under the same conditions of the parameters, as the intensity of the random excitation increases, non-trivial steady-state solution fluctuation will become strenuous, which will result in the non-trivial steady-state solution lose stability and the trivial steady-state solution can be a possible. In the case of parametric principal resonance, the stochastic jump is observed for the first mode, which indicates that the stationary joint probability density concentrates at the non-trivial solution branch when the random excitation is small, but with the increase of intensity of the random excitation, the probability of the trivial steady-state solution will become larger. This phenomenon of stochastic jump can be defined as a stochastic bifurcation.
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