体积分数随机场作用下复合材料层合板固有振动特性不确定性分析  

Uncertainty analysis of natural vibration characteristics of composite laminated plates with spatially varied stochastic volume fractions

作　　者：于汝雨 张旭方[1] YU Ruyu;ZHANG Xufang(School of Mechanical Engineering and Automation,Northeastern University,Shenyang 110819,China)

机构地区：[1]东北大学机械工程与自动化学院,沈阳110819

出　　处：《复合材料学报》2022年第1期412-423,共12页Acta Materiae Compositae Sinica

基　　金：国家自然科学基金(51775095);中央高校基本科研业务费项目(N2003029)。

摘　　要：考虑复合材料层合板中每层体积分数空间不确定性的影响,采用指数型自相关函数模拟每层体积分数同空间位置的依赖关系,结合伽辽金-里兹正交多项式逼近和K-L展开方法,研究了体积分数随机场的自相关长度特征对材料属性随机场离散精度的影响;进而通过体积分数随机场作用下复合材料层合板的随机有限元模型,研究了T300碳纤维/QY8911环氧树脂复合材料垂尾蒙皮结构的固有频率均值、标准差和变异系数与层合板层数之间的关系,基于Monte-Carlo模拟方法验证了采用本文方法开展复合材料层合板固有振动特性分析的有效性。数值结果表明:复合材料层合板结构固有频率的变异系数随铺层数减少而增大,层数越少,纤维体积分数的不确定性对固有振动特性分散性的影响越大。In each layer of the composite laminate,the spatial uncertainty effect of the volume fraction was considered.Using exponential autocorrelation function,the relationship between the volume fraction of each layer and the spatial position was simulated.Combining the Galerkin-Riza discretization and K-L series expansion methods,the influence of autocorrelation length on the discretization accuracy was carried out.The stochastic finite element model of composite laminates with spatially random material properties was established.Taking the T300 carbon fiber/QY8911 epoxy aircraft vertical tail thin-gauge skin structure as an example,the relationships between the mean value,standard deviation and coefficient of variation of the natural frequency and the number of laminate layers were obtained.And the Monte-Carlo simulation method was used to verify the effectiveness of the method in this paper to carry out the natural frequency and mode uncertainty analysis of composite laminates.The results show that:the coefficient of variation of the natural frequency of the composite laminate structure increases with the decrease of the number of layers,and the less the number of layers,the greater influence of uncertainty of the fiber volume fraction on dispersion of the natural vibration characteristics.

关 键 词：体积分数随机场 不确定性分析 固有振动特性 复合材料层合板 随机有限元法 

分 类 号：TB333[一般工业技术—材料科学与工程]