非弹性碰撞振动系统的首次穿越分析

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摘要对高斯白噪声激励作用下的非弹性碰撞振动系统的首次穿越问题作了分析，得到了非弹性碰撞振动系统的条件可靠性函数和相应的条件概率密度函数。不同于以往碰撞物理模型，非弹性碰撞作用采用了修正赫兹接触模型。首先，基于能量耗散平衡法，将碰撞振动系统转化为不含碰撞的等效非线性系统。其次，应用基于系统能量的随机平均法，得到关于系统总能量的平均伊藤随机微分方程。然后，建立条件可靠性函数的控制方程及相应的初边界条件，并数值求解。最后，分析了不同系统参数情形下条件可靠性函数及相应的条件概率密度函数的变化规律。本方法可有效分析非弹性碰撞振动系统的首次穿越问题，数值分析结果表明较大的阻尼系数可提高系统可靠性，而较大的激励强度则往往增加发生首次穿越的概率。

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关键词 ：非弹性碰撞振动系统, 修正赫兹接触模型, 随机平均法, 条件可靠性函数, 条件概率密度函数

Abstract：

The first-passage failure of the inelastic vibro-impact system is studied in this paper, and the conditional reliability function and the conditional probability density function are derived. Different from the traditional impact model, the modified Hertzian contact model is adopted. First, based on the energy dissipation balance technique, the inelastic vibro-impact system is transformed to an equivalent nonlinear system without impact. Second, the averaged Ito differential equation is derived by the stochastic averaging. Third, the governing equation of the conditional reliability function is established and numerically solved under given initial and boundary conditions. Last, the influences of the different system parameters on system reliability and probability density are discussed. The proposed technique is very efficient and accurate for the first passage failure of the vibro-impact system, and the weak excitation intensity and big damping coefficient will enhance the system reliability.

Key words： inelastic vibro-impact system modified Hertzian contact model stochastic averaging the conditional reliability function the conditional probability density

收稿日期: 2015-05-19 出版日期: 2016-08-25

引用本文:

徐明 1，2，金华斌 1，2. 非弹性碰撞振动系统的首次穿越分析[J]. 振动与冲击, 2016, 35(17): 197-200.
Xu Ming1, 2 Jin Hua-bin 1,2 . First-passage failure of the non-inelastic vibro-impact system. JOURNAL OF VIBRATION AND SHOCK, 2016, 35(17): 197-200.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2016/V35/I17/197

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