In this work, stochastic perturbation-based vibration characteristics of cracked bi-material and functionally graded material (FGM) domain with uncertain material properties are investigated using the extended finite element method. The level set function is implemented to track the geometrical discontinuities. The partition of unity-based extrinsic enrichment technique is employed to model the crack and material interface. The exponential law is used to model the graded material properties of FGM. The First-order perturbation technique (FOPT) is implemented to predict the standard deviation of natural frequency for the given uncertainties in the material properties. The numerical results are presented to show the effect of geometrical discontinuities and material randomness on vibration characteristics.

中文翻译：

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裂纹功能梯度和双材料结构固有频率的随机扩展有限元实现

在这项工作中，使用扩展有限元方法研究了具有不确定材料特性的破裂双材料和功能梯度材料 (FGM) 域的基于随机扰动的振动特性。水平集函数用于跟踪几何不连续性。采用基于统一的外在富集技术的划分来模拟裂纹和材料界面。指数定律用于模拟 FGM 的渐变材料特性。采用一阶微扰技术 (FOPT) 来预测材料特性中给定不确定性的固有频率的标准偏差。数值结果展示了几何不连续性和材料随机性对振动特性的影响。