基于能量法的机械系统受振动时的可靠性分析

The reliability analysis of a mechanical system under vibration based on energy method

研究非线性机械系统受振动时 ,特别是受随机振动时的失效分析计算问题。对于受冲击式振动的机械系统定义了系统缓冲系数 ,从能量平衡的角度计算确定非线性系统所需的缓冲长度 ;对于受随机振动的非线性机械系统 ,通过引进 Van der Pol变换 ,采用计算平均功率的方法 ,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 ,求解该方程 ,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 mechanical system subjected to vibrations, especially subjected to random vibrations. For a mechanical system under the effect of impact, a kind of cushioning coefficient is introduced. The cushioning length is determined on the balance of its energy. For a non-linear mechanical system excited randomly, 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 aplication of the Crossing Analysis Techinique and the Miner Criteria, either the fatique failure probability of the system or its average failure time caused by random vibrations can be calculated.