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宽带噪声激励下碰撞摩擦系统的随机响应和稳定性的研究

马兰 田丽丽 刘莉

马兰, 田丽丽, 刘莉. 宽带噪声激励下碰撞摩擦系统的随机响应和稳定性的研究[J]. 应用数学和力学, 2024, 45(9): 1235-1242. doi: 10.21656/1000-0887.440313
引用本文: 马兰, 田丽丽, 刘莉. 宽带噪声激励下碰撞摩擦系统的随机响应和稳定性的研究[J]. 应用数学和力学, 2024, 45(9): 1235-1242. doi: 10.21656/1000-0887.440313
MA Lan, TIAN Lili, LIU Li. Stochastic Responses and Stability Analysis of Vibro-Impact Systems With Friction Under Wideband Noise Excitation[J]. Applied Mathematics and Mechanics, 2024, 45(9): 1235-1242. doi: 10.21656/1000-0887.440313
Citation: MA Lan, TIAN Lili, LIU Li. Stochastic Responses and Stability Analysis of Vibro-Impact Systems With Friction Under Wideband Noise Excitation[J]. Applied Mathematics and Mechanics, 2024, 45(9): 1235-1242. doi: 10.21656/1000-0887.440313

宽带噪声激励下碰撞摩擦系统的随机响应和稳定性的研究

doi: 10.21656/1000-0887.440313
基金项目: 

宁夏自然科学基金 2020AAC03064

国家自然科学基金 12262032

详细信息
    作者简介:

    马兰(2000—),女(E-mail: ml2676649359@163.com)

    通讯作者:

    刘莉(1979—),女,副教授,博士(通讯作者. E-mail: liuli0951@126.com)

  • 中图分类号: O211.63

Stochastic Responses and Stability Analysis of Vibro-Impact Systems With Friction Under Wideband Noise Excitation

  • 摘要: 研究了宽带噪声激励下碰撞摩擦系统的随机响应和概率为1渐近稳定性. 基于非光滑变换和随机平均法得到了碰撞摩擦系统响应的稳态概率密度,并通过与Monte Carlo数值模拟结果对比,验证了上述解析方法的有效性. 讨论了摩擦力和碰撞恢复系数对系统稳态概率密度的影响. 基于平均Itô微分方程,得到其线性化方程的最大Lyapunov指数的表达式,通过Lyapunov指数确定系统平凡解的稳定性. 结果表明,改变碰撞恢复系数和摩擦系数能调整系统的随机稳定性.
  • 图  1  不同摩擦系数下系统稳态响应的概率密度函数

       为了解释图中的颜色,读者可以参考本文的电子网页版本,后同.

    Figure  1.  PDFs of system responses under different values of μ

    图  2  不同碰撞系数下系统稳态响应的概率密度函数

    Figure  2.  PDFs of system responses under different values of r

    图  3  不同非线性阻尼系数βγ下系统稳态响应的概率密度函数

    Figure  3.  PDFs of system responses under different values of β and γ

    图  4  Lyapunov指数随碰撞恢复系数r和随摩擦系数μ的变化

    Figure  4.  The variations of TLE with r and μ

    图  5  系统在(r, μ)平面内的概率为1渐近稳定区域

    Figure  5.  The asymptotic stability region with probabilityone on the plane of (r, μ)

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出版历程
  • 收稿日期:  2023-10-18
  • 修回日期:  2024-05-12
  • 刊出日期:  2024-09-01

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