Stochastic responses of a viscoelastic-impact system under additive and multiplicative random excitations
Stochastic responses of a viscoelastic-impact system under additive and multiplicative random excitations
复制标题
加法和乘法随机激励下粘弹性冲击系统的随机响应
DOI：
10.1016/j.cnsns.2015.11.008
复制
发表时间：
2016
影响因子：
3.9
通讯作者：
Wang Xiying
中科院分区：
文献类型：
--
作者：
Zhao Xiangrong;Xu Wei;Yang Yongge;Wang Xiying
本文研究了粘弹性碰撞系统在加性和乘性随机激励下的随机响应。粘弹性力由刚度和阻尼项的组合来代替。利用状态变量的非光滑变换将原系统变换为不含冲击项的新系统。应用随机平均法得到稳态概率密度函数。通过与数值计算结果的比较，验证了解析方法的有效性。指出恢复系数、粘弹性参数和阻尼系数都能引起随机P分叉的发生。此外，联合平稳概率密度函数的三个峰值进行了探索。
This paper deals with the stochastic responses of a viscoelastic-impact system under additive and multiplicative random excitations. The viscoelastic force is replaced by a combination of stiffness and damping terms. The non-smooth transformation of the state variables is utilized to transform the original system to a new system without the impact term. The stochastic averaging method is applied to yield the stationary probability density functions. The validity of the analytical method is verified by comparing the analytical results with the numerical results. It is invaluable to note that the restitution coefficient, the viscoelastic parameters and the damping coefficients can induce the occurrence of stochastic P-bifurcation. Furthermore, the joint stationary probability density functions with three peaks are explored.