This study proposes an effective approach for stochastic natural frequency analysis of axially varying functionally graded material (FGM) pipes conveying fluid. The Karhunen-Loève expansion is first employed to generate a random filed with axially varying FGM properties. Then the input uncertainty is substituted into the governing equation of axially varying FGM pipes conveying fluid. The stochastic differential quadrature method is introduced to derive the generalized eigenvalue equation and obtain the natural frequencies. Based on the established stochastic mechanical model, the statistical characteristics of the stochastic natural frequency response can be estimated. In order to mitigate the calls of the mechanical model, a Kriging model requiring a rather small design of experiment is utilized to mimic the true mechanical model. An approach combining the material random field, the derived generalized eigenvalue equation and the Kriging model is finally proposed. The example investigations have validated the effectiveness as well as the efficiency of the proposed strategy for stochastic natural frequency analysis of axially varying FGM pipes conveying fluid with random material properties.

这项研究提出了一种有效的方法，用于对轴向变化的功能梯度材料（FGM）输送流体的管道进行随机自然频率分析。首先使用Karhunen-Loève展开来生成具有轴向变化的FGM属性的随机场。然后，将输入不确定性代入轴向变化的FGM管道输送流体的控制方程中。引入随机微分正交方法推导广义特征值方程并获得固有频率。基于建立的随机力学模型，可以估算随机自然频率响应的统计特性。为了减轻机械模型的影响，使用了需要进行相当小的实验设计的Kriging模型来模拟真实的机械模型。最后提出一种结合材料随机场，导出的广义特征值方程和Kriging模型的方法。实例研究已经验证了所提出的策略对轴向变化的FGM管道输送随机材料特性的FGM管道进行随机固有频率分析的有效性和效率。