Natural frequency analysis of functionally graded material beams with axially varying stochastic properties
Natural frequency analysis of functionally graded material beams with axially varying stochastic properties
复制标题
具有轴向变化随机特性的功能梯度材料梁的固有频率分析
DOI：
10.1016/j.apm.2018.10.011
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发表时间：
2019
影响因子：
5
通讯作者：
Zhang Xufang
中科院分区：
文献类型：
--
作者：
Zhou Yangjunjian;Zhang Xufang
功能梯度材料（FGM）由于其优异的热学和动力学特性，有可能在工程现实中取代普通材料。在这方面，本文提出了一种对具有轴向变化材料特性的组合梁进行不确定固有频率分析的有效方法。我们不是简单地将材料模型假设为确定性函数，而是进一步将 FGM 属性扩展为随机场，它能够解释实验室观察和现场数据的空间变异性。由于轴向变化的输入不确定性，随机 FGM (S-FGM) 梁的固有频率成为随机变量。为此，首先引入 Karhunen-Loève 展开式将复合材料随机场表示为有限数量的随机变量的总和。然后，推导了广义特征值函数，用于组合梁的随机固有频率分析。一旦获得了机械模型，就可以使用类似于实验设计的残酷蒙特卡罗模拟（MCS）来估计不确定固有频率响应的统计特性。为了减轻MCS方法的计算成本，使用基于相当少量的训练样本开发的广义多项式混沌展开模型来模拟真实的固有频率函数。案例研究证明了所提出的方法对于具有轴向变化随机属性的功能梯度材料梁的不确定固有频率分析的有效性。
The functionally graded material (FGM) has a potential to replace ordinary ones in engineering reality due to its superior thermal and dynamical characteristics. In this regard, the paper presents an effective approach for uncertain natural frequency analysis of composite beams with axially varying material properties. Rather than simply assuming the material model as a deterministic function, we further extend the FGM property as a random field, which is able to account for spatial variability in laboratory observations and in-field data. Due to the axially varying input uncertainty, natural frequencies of the stochastically FGM (S-FGM) beam become random variables. To this end, the Karhunen–Loève expansion is first introduced to represent the composite material random field as the summation of a finite number of random variables. Then, a generalized eigenvalue function is derived for stochastic natural frequency analysis of the composite beam. Once the mechanistic model is available, the brutal Monte-Carlo simulation (MCS) similar to the design of experiment can be used to estimate statistical characteristics of the uncertain natural frequency response. To alleviate the computational cost of the MCS method, a generalized polynomial chaos expansion model developed based on a rather small number of training samples is used to mimic the true natural frequency function. Case studies have demonstrated the effectiveness of the proposed approach for uncertain natural frequency analysis of functionally graded material beams with axially varying stochastic properties.