随机窄带噪声作用下非线性碰撞振动系统的稳态响应研究

黄冬梅; 徐伟

doi:10.3879/j.issn.1000-0887.2016.06.009

随机窄带噪声作用下非线性碰撞振动系统的稳态响应研究

doi: 10.3879/j.issn.1000-0887.2016.06.009

黄冬梅,
徐伟

西北工业大学应用数学系, 西安 710072

基金项目: 国家自然科学基金（11472212；11532011）

详细信息

作者简介:
黄冬梅（1988—），女，博士生(通讯作者. E-mail: dongmeihuang1@hotmail.com).

中图分类号: O324
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- 被引次数: 0
出版历程
- 收稿日期: 2016-01-04
- 修回日期: 2016-02-21
- 刊出日期: 2016-06-15

Dynamic Responses of Nonlinear Vibro-Impact Systems Under Narrow-Band Random Parametric Excitation

Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, P.R.China

Funds: The National Natural Science Foundation of China（11472212；11532011）

摘要

摘要: 研究了随机参激作用下一个非线性碰撞振动系统的随机响应.基于Krylov-Bogoliubov平均法，借助第一类改进的Bessel函数，得到了决定平凡解的几乎确定稳定性的最大Lyapunov指数.模拟结果发现，碰撞振动系统的最大Lyapunov指数特性不同于一般的非碰撞系统，其最小值为负.同时，在确定性情形下，得到了骨架曲线方程和不稳定区域的临界方程.进一步，利用矩方法，讨论了系统的一阶和二阶非平凡稳态矩，发现了碰撞振动系统中有频率岛现象的存在.最后，借助Fokker-Planck-Kolmogorov方程，利用有限差分法，讨论了碰撞振动系统中存在的随机跳现象.在随机强度较小时，稳态概率密度集中于响应振幅的非平凡分支；但是随着随机强度的增加，平凡稳态解的概率会变大.
- 碰撞振动系统 /
- 非光滑变化 /
- 稳态解 /
- 随机跳 /
- 窄带随机噪声
Abstract: The stochastic responses of nonlinear vibro-impact systems under random parametric excitation were investigated. Based on the Krylov-Bogoliubov averaging method, the largest Lyapunov exponent deciding the almost sure stability of the trivial solution was derived. Results show that the characteristics of the largest Lyapunov exponent of the vibro-impact system was different from that of the system without impact. Meanwhile, the backbone curve and the critical equation for the unstable region were also derived in the deterministic case. Then, the 1st- and 2nd-order non-trivial steady-state moments of the system were discussed, and the frequency island phenomenon was also found. Finally, the phenomenon of stochastic jump was analyzed via the finite difference method. The basic jump phenomena indicate that, under the conditions of system parameters within a smaller bandwidth, the most probable motion is around the non-trivial branch of the amplitude response curve, whereas within a larger bandwidth, the most probable motion is around the trivial one of the amplitude response curve.
- vibro-impact system /
- non-smooth transformation /
- steady-state behavior /
- stochastic jump /
- narrow-band random noise

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