橡胶材料具有高弹性、大变形和阻尼特性，由此表现出良好的减振、隔振和缓冲性能而被广泛应用于各类工业产品中。航空航天飞行器的惯导系统上大量使用的硅橡胶减振器元件，在实际工作条件下处于复杂的随机振动环境，橡胶材料的疲劳寿命是制约橡胶减振元件使用的重要因素，通过仿真的方法研究减振器橡胶的疲劳耐久性、预测橡胶在随机振动条件下的疲劳寿命对橡胶减振器的使用具有重要意义。本文在研究橡胶复杂本构关系理论、疲劳寿命理论和随机振动响应分析方法的基础上，分别提出了基于时域和频域有限元仿真结果，预测减振器橡胶材料在随机振动条件下疲劳耐久性能的方法，并将此方法用于减振器橡胶单元的疲劳寿命分析，取得了显著的效果。本研究首先进行了硅橡胶材料实验，获取了用于模拟橡胶材料复杂本构关系的材料模型参数，另外还获取了用于橡胶材料疲劳寿命计算的橡胶裂纹扩展模型参数，为橡胶减振器有限元仿真和疲劳寿命计算提供参数支持。在此基础上，建立了考虑包括超弹性、粘弹性和阻尼特性在内的材料非线性特性的橡胶减振器有限元模型，采用由减振器加速度功率谱载荷构造成的时域载荷谱作为载荷输入，对橡胶减振器的振动情况进行了有限元仿真，然后基于Will Mars提出的开裂能密度理论和橡胶微裂纹扩展临界平面法，建立了橡胶材料时域疲劳寿命计算模型，分析计算了减振器橡胶单元的疲劳寿命。另一方面，建立了橡胶减振器结构的随机振动仿真模型和频域疲劳损伤计算模型，以减振器疲劳加速度功率谱为载荷输入，模拟了减振器在随机振动条件下的动态响应情况，而后提取橡胶单元应力响应功率谱密度计算结果，计算了频域疲劳损伤模型中的各参数，并计算了减振器橡胶的疲劳损伤分布情况。计算结果表明，减振器在两种模型下的疲劳寿命分布情况具有一致的规律性，两种方法预测出的橡胶单元疲劳危险点位置相同。研究结果对于随机振动条件下橡胶材料的疲劳耐久性能的分析预测具有显著的指导意义。

Rubber is characterized by its high elasticity, large deformability and damping property, thus making it a great material out of which shock absorbers and dampers are made. Dampers consist of silicon rubber are widely used in aeronautics and astronautics, under which situation durability of rubber is a big concern since dampers are subjected to complex loading conditions during the whole life. It is of great importance for the engineers to analyze the fatigue problem of rubber material and predict the fatigue life of rubber component before it comes into products level.In this research, the constitutive behavior of rubber, the fatigue prediction theory and theory of stochastic vibration are taken into consideration. Two methods are propoesd to build the FEA model of the rubber damper in time domain and in frequency domain separately. The fatigue analyses of rubber damper are conducted after the FE analysis. Reasonable results are achieved from the fatigue life prediction of the rubber component.Tests on rubber material are performed at the first place to obtain parameters of material used in FE analysis, including hyper-elasticity, visco-elasticity and fatigue crack growth behavior. Meanwhile acceleration loading sequence is generated from the stochastic loading condition described as acceleration PSD spectrum. Fatigue analysis is conducted based on the CED theory and critical plane analysis using Endurica rubber fatigue analyzer. Fatigue life of each element of rubber is calculated.On the other hand, the FE model of the rubber damper is built for the random vibration analysis, and the stress PSD responses of each element are obtained, upon which the fatigue analysis is conducted based on the frequency domain method. Results show an obvious relativity between time domain method and frequent domain method. Same distribution of the predicted fatigue life demonstrates the validity of these two methods.