随机P-分叉在一个Duffing-van der Pol振动冲击系统与宾汉模型
Zijian Kan1, Jun Wang1,2, Jianchao Zhang1,2
1Department of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China.
Chaos (Woodbury, N.Y.)
|February 5, 2025
概括
这项研究探讨了非线性振荡器中与摩擦和冲击有关的随机P-分叉. 发现阻尼和噪声强度等关键参数触发了这些复杂的动态行为.
科学领域:
- 非线性动力学是一种非线性动力学.
- 随机系统分析 随机系统分析
- 机械振动 - 机械振动
背景情况:
- 具有摩擦和振动冲击的非线性振荡器表现出复杂的动态.
- 随机激发可以显著改变系统行为,导致像分叉这样的现象.
- 分析这些系统需要先进的数学和计算技术.
研究的目的:
- 在高斯白噪声下的宾汉摩擦模型的Duffing-van der Pol振动冲击振荡器中研究静态P-分叉现象.
- 开发和验证一种近似的分析方法,用于分析非线性系统中的随机响应和分叉行为与摩擦和振动冲击.
- 为了确定诱导随机P-分叉的关键参数条件.
主要方法:
- 采用非光滑转换来简化振动冲击振荡器模型.
- 应用随机平均技术来得出平均的随机Itô方程.
- 解决福克-普朗克-科尔摩戈罗夫方程以获得稳定状态概率密度函数.
- 使用奇点理论来推导随机P-分叉的临界参数条件.
- 进行方法验证的数值模拟.
主要成果:
- 提出并验证了一种近似的分析方法,用于分析非线性系统中的随机响应和分叉.
- 基于概率密度函数,推导了随机P-分叉的临界参数条件.
- 两叉图和各种概率密度图构建以说明系统行为.
- 变化的参数,如减噪系数,噪声强度,和振动冲击系数被证明是诱导随机P-分叉.
结论:
- 拟议的分析方法有效地分析了复杂的非线性系统中的随机P-分叉现象.
- 随机P-分叉对多个系统参数的变化很敏感,包括减噪和噪声强度.
- 这项研究为在随机激发下非线性振动冲击系统的动态提供了宝贵的见解.
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