Stochastic response analysis of multi-degree-of-freedom vibro-impact system undergoing Markovian jump
Stochastic response analysis of multi-degree-of-freedom vibro-impact system undergoing Markovian jump
复制标题
马尔可夫跳跃多自由度振动冲击系统随机响应分析
DOI：
10.1007/s11071-020-05823-z
复制
发表时间：
2020-07-27
影响因子：
5.6
通讯作者：
Deng, Zicheng
中科院分区：
文献类型：
--
作者：
Hu, Rongchun;Gu, Xudong;Deng, Zicheng
本文研究了马氏跳跃过程中随机激励的多自由度碰撞振动系统的平稳响应。将子结构突变或外部激励突变的冲击振动系统建模为连续-离散的马尔可夫跳跃系统，这与传统的冲击振动模型有本质的区别。结果表明，随机跳跃因子在有限个模式之间切换。这一显著特征使我们能够将这种类型的动态行为识别为经历马尔可夫跳跃的混合振动-碰撞系统的响应。利用两步近似技术，我们可以将所考虑的多自由度混合系统简化为系统总能量形式的一维平均IT？方程。为了预测原始混杂系统的稳态响应，推导了伴随的Fokker-Planck-Kolmogorov(FPK)系统能量方程的近似解析解。
The paper treats stationary response of a stochastically excited multi-degree-of-freedom (multi-DOF) vibro-impact system undergoing Markovian jump. The vibro-impact system with sudden abrupt changes in substructures or external excitations is modeled as a continuous-discrete Markovian jump system, which is essentially different from the traditional vibro-impact model. It is demonstrated that the random jump factors switch between a finite number of modes. This salient feature allows us to identify this type of dynamic behaviors as response of hybrid vibro-impact systems undergoing Markovian jump. Utilizing a two-step approximate technique, we can reduce the considered multi-DOF hybrid system to one-dimensional averaged Itô equation of the form of system’s total energy. The approximate analytical solution of the associated Fokker–Planck–Kolmogorov (FPK) equation of system’s energy is derived to predict the stationary response of original hybrid systems.