系统受随机激励时的可靠性分析

The Reliability of a Nonlinear System under Random Vibration

主要研究非线性缓冲包装系统受随机激励时的失效分析计算问题 ,非线性缓冲包装系统受随机激励时会产生随机振动响应 ,从而使得非线性缓冲包装系统内部产生随机的交变应力。因交变应力而使非线性缓冲包装系统失效的原因有两种 :第一种是因为应力的幅值超过了缓冲包装系统的许可应力 ;第二种则是随机的交变应力所形成的累积效应使缓冲包装系统产生疲劳破坏。主要研究第二种情况时的失效分析计算问题。对于受随机振动的非线性缓冲包装系统 ,通过引进VanderPol变换 ,采用计算平均输入功率和平均输出功率的方法 ,发现在一定条件下 ,系统新的变量将趋于一个联合马可夫过程 ,从而可建立起相应的FPK方程 ,通过求解该FPK方程 ,采用穿越分析技术和Miner准则 ,可计算出系统因随机振动而导致的疲劳破坏概率或平均失效时间。

This paper mainly deals with the failure analysis and calculation of a non-linear packaging cushioning system subject to random vibrations.A non-linear packaging cushioning system will give out random vibration responses when the system is excited randomly,and cause some alternative changing stress inside the non-linear packaging cushionig system.There are two causes that make non-linear packaging cushioning system fail.One is the amplitude of the stress exceeding the permission value of the non-linear packaging cushioning system,the other is the fatigue failure caussed by the accumulative effects of the random alternative stress.The emphases of the research are put on the failure analysis and calculation of the nonlinear system under the second condition.For a non-linear packaging cushioning system subject to random excitations,after the Van der Pol transformation is adopted and the average power calculation method is used,it is found that the new variables of the system will trend to a Markov Process under certain conditions.The corresponding FPK equations can be set up.Through the resolution of these FPK equations,the application of the Crossing Analysis Technique and the Miner Criteria,either the fatigue failure probability of the packaging system or its average failure time caused by random vibrations can be calculated.